First slide

Simple harmonic motion

Question

The maximum acceleration of a body moving in SHM is a₀ and maximum velocity is v₀. The amplitude is given by

Moderate

A

$\frac{v_{0}^{2}}{a_{0}}$
B

$a_{0} V_{0}$
C

$\frac{a_{0}^{2}}{v_{0}}$
D

$\frac{1}{a_{0} v_{0}}$

Solution

Maximum acceleration, $a_{0} = ω^{2} A$
and maximum velocity, $V_{0} = A ω \Rightarrow v_{0}^{2} = A^{2} ω^{2}$
On dividing, $\frac{a_{0}}{v_{0}^{2}} = \frac{1}{A} or A = \frac{v_{0}^{2}}{a_{0}}$

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