1. Phys 250 Ch14 p1 Chapter 13: Periodic Motion What we already know: Elastic Potential Energy energy stored in a stretched/compressed spring Force: Hooke’s Law F = kx k = spring constant F = 0 F = k x/2 F = k x x unstretched half stretched stretched

2. Phys 250 Ch14 p2 Oscillations: Stable Equilibrium: U  ½kx 2 F   kx (small) displacement from equilibrium generates restoring force inertia apply F = ma Amplitude A = maximum displacement from equilibrium Period T = time for one full cycle Frequency f = number of cycles per unit time = 1/T A AA A U U x

3. Phys 250 Ch14 p3 Example(14.2): A spring with a spring constant of 9.5 N/m is placed horizontally. A 0.35 kg block is placed at the end of the spring and the spring is compressed 6.0 cm. What is the initial force on the block? What is the initial acceleration of the block? Example: What is the natural frequency of oscillation for the mass-spring combination in the previous example? What s the period of oscillations?

4. Phys 250 Ch14 p4 Using Conservation of energy: Position, speed and acceleration in simple harmonic motion x t maximum speed at x = 0 Amplitude A = x max (x 0 } v = 0 when x = x max x = A cos 2  ft

5. Phys 250 Ch14 p5 Example: A mass of 0.35 kg oscillates on a spring with a spring constant of 9.5 N/m. If the spring is initially compressed by 5cm and released from rest. -What is the energy of the oscillations? -What is the maximum speed of the mass? -What is the speed of the mass when it is 3cm from equilibrium?

6. Phys 250 Ch14 p6 The Simple Pendulum mass m on a string of length L x s mg T F net L L Example: How long should a pendulum be in order to have a period of 1.0 s?