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Simple Harmonic Motion

A humbling fraction of physics boils down to direct application of simple harmonic motion, the description of oscillating objects. Learn the basis for springs, strings, and quantum fields.

Simple Harmonic Motion - Problem Solving


A body executing linear simple harmonic motion has a velocity of \( 7.0 \text{ cm/s} \) when its displacement is \( 2.0 \text{ cm}, \) and a velocity of \( 2.0 \text{ cm/s} \) when its displacement is \( 7.0 \text{ cm}. \) What is the square of the amplitude of oscillation?

A body executing linear simple harmonic motion has a velocity of \( 8.0 \text{ cm/s} \) when its displacement is \( 3.0 \text{ cm}, \) and a velocity of \( 3.0 \text{ cm/s} \) when its displacement is \( 8.0 \text{ cm}. \) If the mass of the oscillator is \( 5.0 \text{ kg}, \) what is the approximate total energy of the oscillator?

Not every oscillation in nature is a harmonic oscillation - in this problem, we will examine a non-harmonic oscillation. Suppose we had a rubber ball with a perfect coefficient of restitution so that, when dropped, it would always return to the same height. The period of the bouncing is the time \(T\) between successive bounces and the amplitude \(A\) of this non-linear oscillation is the maximum height of the ball above the floor. For a harmonic oscillator, the period and amplitude are independent, but not so here. Instead, there's a relation between them: \(T\) proportional to \(A^w\). Find \(w\).

Two blocks, each of mass \( m = 2.0 \text{ kg},\) are connected by a spring of force constant \( k = 3.0 \text{ N/m} \) and placed on a horizontal frictionless surface, as shown in the above diagram. If an equal force of \( F = 2.0 \text{ N} \) is applied to each block in the direction of arrow, what is the approximate time period of the system when the force is removed?

You bounce on a huge trampoline and start oscillating up and down with a period of \(3~\mbox{s}\). After a long while, you come to rest but the trampoline below you is displaced below its natural height. How much is the trampoline bent in m?

Details and assumptions

  • Model the trampoline as a spring.

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