AP Physics Review Ch 10 – Oscillatory Motion Simple Harmonic Motion  repetitive motion that follows Hooke’s Law; Fs = -kx Know where net force, acceleration, and speed are maximum values and where they are zero; be able to calculate the maximum values for a mass oscillating on the end of a spring (conservation of mechanical energy for speed, Hooke’s law for force, and Newton’s 2nd law for acceleration) Understand the position versus time graph for an object oscillating with SHM 𝑥=𝐴 cos 𝜔𝑡 𝐴amplitude 𝜔= 2𝜋 𝑇 =2𝜋𝑓 Understand the energy transformations for an object oscillating with SHM; be able to use conservation of mechanical energy to calculate speed or amplitude 𝐸 𝑚𝑒𝑐ℎ =𝐾+𝑈 and 𝐾=0 @ 𝐴 (amplitude) so 𝐸 𝑚𝑒𝑐ℎ = 1 2 𝑘 𝐴 2 Understand the graphs for energy and force with respect to position for an object undergoing SHM Understand the motion of a simple pendulum at small angles; be able to use conservation of mechanical energy to find speed of a simple pendulum at the bottom of the swing; be able to use Newton’s 2nd law to determine the tension in the string at the bottom of the swing knowing that the acceleration is centripetal Know the factors that affect the period (or frequency) of a spring and pendulum 𝑇 𝑆 =2𝜋 𝑚 𝑘 𝑇 𝑃 =2𝜋 𝑙 𝑔 𝑇= 1 𝑓 Understand everything we have covered this year in physics including projectile motion, Newton’s laws (calculate force and acceleration), conservation of energy, conservation of momentum, and circular motion

Speed is a maximum; net force is zero. This is the position graph of a mass on a spring. What can you say about the speed and the magnitude of the net force at the instant indicated by the dotted line? Speed is a maximum; net force is zero. Speed is zero; net force is zero. Speed is a maximum; net force is a maximum. Speed is zero; net force is a maximum. STT14.4

Speed is a maximum; net force is zero. This is the position graph of a mass on a spring. What can you say about the speed and the magnitude of the net force at the instant indicated by the dotted line? Speed is a maximum; net force is zero. Speed is zero; net force is zero. Speed is a maximum; net force is a maximum. Speed is zero; net force is a maximum. STT14.4

A mass oscillates on a horizontal spring A mass oscillates on a horizontal spring. It’s velocity is vx and the spring exerts force Fx. At the time indicated by the arrow, vx is  and Fx is  vx is  and Fx is – vx is – and Fx is 0 vx is 0 and Fx is  vx is 0 and Fx is – Answer: C 4

A mass oscillates on a horizontal spring A mass oscillates on a horizontal spring. It’s velocity is vx and the spring exerts force Fx. At the time indicated by the arrow, vx is  and Fx is  vx is  and Fx is – vx is – and Fx is 0 vx is 0 and Fx is  vx is 0 and Fx is – 5

A mass oscillates up and down on a spring; the motion is illustrated at right. At which time or times shown is the acceleration zero? At which time or times shown is the kinetic energy a maximum? At which time or times shown is the potential energy a maximum? Answers: 1: A, C, E 2: A, C, E 3: B, D .

A mass oscillates up and down on a spring; the motion is illustrated at right. At which time or times shown is the acceleration zero? At which time or times shown is the kinetic energy a maximum? At which time or times shown is the potential energy a maximum? A, C, E A, C, E B, D

A mass on a spring in SHM has amplitude A and period T A mass on a spring in SHM has amplitude A and period T. At what point in the motion is v = 0 and a = 0 simultaneously? (A) x = A (B) x > 0 but x < A (C) x = 0 (D) x < 0 (E) none of the above

A mass oscillates in simple harmonic motion with amplitude A A mass oscillates in simple harmonic motion with amplitude A. If the mass is doubled, but the amplitude is not changed, what will happen to the total energy of the system? (A) total energy will increase (B) total energy will not change (C) total energy will decrease

If the amplitude of a simple harmonic oscillator is doubled, which of the following quantities will change the most? (A) frequency (B) period (C) maximum speed (D) maximum acceleration (E) total mechanical energy

Two identical blocks oscillate on different horizontal springs Two identical blocks oscillate on different horizontal springs. Which spring has the larger spring constant? The red spring The blue spring There’s not enough information to tell. Answer: A 11

Two identical blocks oscillate on different horizontal springs Two identical blocks oscillate on different horizontal springs. Which spring has the larger spring constant? The red spring The blue spring There’s not enough information to tell. 12

A block of mass m oscillates on a horizontal spring with period T  2 A block of mass m oscillates on a horizontal spring with period T  2.0 s. If a second identical block is glued to the top of the first block, the new period will be 1.0 s 1.4 s 2.0 s 2.8 s 4.0 s Answer: D 13

A block of mass m oscillates on a horizontal spring with period T  2 A block of mass m oscillates on a horizontal spring with period T  2.0 s. If a second identical block is glued to the top of the first block, the new period will be 1.0 s 1.4 s 2.0 s 2.8 s 4.0 s 14

A glider with a spring attached to each end oscillates with a certain period. If identical springs are added in parallel to the original glider, what will happen to the period? (A) period will increase (B) period will not change (C) period will decrease

A mass oscillates on a vertical spring with period T A mass oscillates on a vertical spring with period T. If the whole setup is taken to the Moon, how does the period change? (A) period will increase (B) period will not change (C) period will decrease

A pendulum is pulled to the side and released A pendulum is pulled to the side and released. The mass swings to the right as shown. The diagram shows positions for half of a complete oscillation. At which point or points is the speed the highest? At which point or points is the acceleration the greatest? At which point or points is the restoring force the greatest? Answers: 1: C 2: A, E 3: A, E

A pendulum is pulled to the side and released A pendulum is pulled to the side and released. The mass swings to the right as shown. The diagram shows positions for half of a complete oscillation. At which point or points is the speed the highest? At which point or points is the acceleration the greatest? At which point or points is the restoring force the greatest? C A, E A, E

A series of pendulums with different length strings and different masses is shown below. Each pendulum is pulled to the side by the same (small) angle, the pendulums are released, and they begin to swing from side to side. Which of the pendulums oscillates with the highest frequency? Answer: A

A series of pendulums with different length strings and different masses is shown below. Each pendulum is pulled to the side by the same (small) angle, the pendulums are released, and they begin to swing from side to side. Which of the pendulums oscillates with the highest frequency? A

Two pendula have the same length, but different masses attached to the string. How do their periods compare? (A) period is greater for the greater mass (B) period is the same for both cases (C) period is greater for the smaller mass

Two pendula have different lengths: one has length L and the other has length 4L. How do their periods compare? (A) period of 4L is four times that of L (B) period of 4L is two times that of L (C) period of 4L is the same as that of L (D) period of 4L is one-half that of L (E) period of 4L is one-quarter that of L

A grandfather clock has a weight at the bottom of the pendulum that can be moved up or down. If the clock is running slow, what should you do to adjust the time properly? (A) move the weight up (B) move the weight down (C) moving the weight will not matter (D) call the repair man

A swinging pendulum has period T on Earth A swinging pendulum has period T on Earth. If the same pendulum were moved to the Moon, how does the new period compare to the old period? (A) period increases (B) period does not change (C) period decreases

After a pendulum starts swinging, its amplitude gradually decreases with time because of friction. What happens to the period of the pendulum during this time? (A) period increases (B) period does not change (C) period decreases

What is the spring constant of a spring that stretches 2 What is the spring constant of a spring that stretches 2.00 cm when a mass of 0.600 kg is suspended from it? Use 9.8 m/s2 for gravity. (A) 0.300 N/m (B) 30.0 N/m (C) 2.94 N/m (D) 294 N/m

A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration? (A) 0.024 m (B) 0.058 m (C) 0.24 m (D) 0.58 m

A 2.0-kg mass is attached to the end of a horizontal spring of spring constant 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is the total mechanical energy of this system? (A) 0.020 J (B) 25 J (C) 0.25 J (D) 1.0 J

A 4. 0-kg object is attached to a spring of spring constant 10 N/m A 4.0-kg object is attached to a spring of spring constant 10 N/m. The object is displaced by 5.0 cm from the equilibrium position and let go. What is the period of vibration? (A) 2.0 s (B) 4.0 s (C) 8.0 s (D) 16 s

A pendulum has a period of 2.0 s on Earth. What is its length? (A) 2.0 m (B) 1.0 m (C) 0.70 m (D) 0.50 m

The pendulum of a grandfather clock is 1. 0 m long The pendulum of a grandfather clock is 1.0 m long. What is its period on the Moon where the acceleration due to gravity is only 1.7 m/s2? (A) 1.2 s (B) 2.4 s (C) 4.8 s (D) 23 s

A block oscillates on a very long horizontal spring A block oscillates on a very long horizontal spring. The graph shows the block’s kinetic energy as a function of position. What is the spring constant? 1 N/m 2 N/m 4 N/m 8 N/m Answer: C 32

A block oscillates on a very long horizontal spring A block oscillates on a very long horizontal spring. The graph shows the block’s kinetic energy as a function of position. What is the spring constant? 1 N/m 2 N/m 4 N/m 8 N/m 33

A set of springs all have initial length 10 cm A set of springs all have initial length 10 cm. Each spring now has a mass suspended from its end, and the different springs stretch as shown below. Now, each mass is pulled down by an additional 1 cm and released, so that it oscillates up and down. Which of the oscillating systems has the highest frequency? Answer: C .

A set of springs all have initial length 10 cm A set of springs all have initial length 10 cm. Each spring now has a mass suspended from its end, and the different springs stretch as shown below. Now, each mass is pulled down by an additional 1 cm and released, so that it oscillates up and down. Which of the oscillating systems has the highest frequency? C C