First slide

Simple hormonic motion

Question

A particle is executing simple harmonic motion along a straight line with amplitude 2 cm. Maximum restoring force acting on the particle is 2N. Find the distance of the particle from the equilibrium position when restoring force acting on the particle is 1N.

Difficult

A

0.25 cm
B

0.5 cm
C

1 cm
D

0.75 cm

Solution

Restoring force $F = m (ω^{2} x) = (m . ω^{2} A) . (\frac{x}{A}) = F_{m} (\frac{x}{A})$
$\Rightarrow x = (\frac{F}{F_{m}}) A = \frac{1}{2} (2) cm = 1 cm$

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