First slide

Simple harmonic motion

Question

Potential energy of a particle executing SHM is U at an instant. Magnitude of acceleration is a at the same instant. If x is the magnitude of displacement of the particle

Easy

A

U is proportional to x
B

a is proportional to x
C

U is proportional to x²
D

Both (2) and (3)

Solution

For simple harmonic motion, the potential energy can be written as $U = \frac{1}{2} K x^{2}; ∴ U α x^{2}$ . Differentiating with respect to x we get $\frac{d U}{d x} = - K x$ .
Here $\frac{d U}{d x}$ is the force due to simple harmonic motion which can be equated to ma. Hence we get $m a = - K x$ .
From this we can conclude that $a = \frac{- K x}{m} ∴ a α x$

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