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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 coefficient 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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