Simple Harmonic Motion Oscillations Simple Harmonic Motion

Examples of Simple Harmonic Motion The weight mg of the mass is balanced by the tension T in the spring. When the spring is extended by an amount Δx, as shown, there is an additional upward force in the spring given by 𝐹= −𝑘∆𝑥 where k is a constant of the spring.

Spring Constant Every spring has a spring constant, it is based on the stiffness of the spring. The stiffer the spring, the higher the value of k. K is given by 𝑘= 𝐹 ∆𝑥 Units: 𝑁𝑚 −1

Period T For a mass m suspended from a light spring having spring constant k, the period T of the oscillations is given by 𝑇=2𝜋 𝑚 𝑘

Simple Pendulum A simple pendulum is a point mass m on a light, inelastic string. When the pendulum is pulled an angle and released, there will be a restoring force acting in the direction of the equilibrium position.

Simple Pendulum Because the simple pendulum moves in the arc of a circle, the displacement will be an angular displacement θ, rather than a linear displacement x. Forces acting on the pendulum is the weight mg and the tension T in the string. Component of the weight along the direction of the string is 𝑚𝑔 cos 𝜃 Component of the weight at right angles to the direction of the spring is the restoring force 𝑚𝑔 sin 𝜃

Period The period T of the oscillation is related to the length l of the pendulum. (l is the distance between the center of mass of the pendulum and the point of suspension) 𝑇=2𝜋 𝑙 𝑔 g is the acceleration of free fall.

Example

Example

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