First slide

Simple harmonic motion

Question

The maximum acceleration of a particle in SHM is made four times keeping the maximum speed to be constant. It is possible when

Moderate

A

amplitude of oscillation is doubled while frequency remains constant
B

amplitude of oscillation is doubled while frequency is halved
C

amplitude of oscillation is made one-fourth while frequency is made four times
D

amplitude of oscillation remains constant while frequency is doubled

Solution

$\begin{array}{l} a_{max} = A ω^{2} . . . . . . (1) \\ v_{max} = A ω . . . . . . . . (2) \\ \Rightarrow a_{max} = v_{max} ω \end{array}$
Since, $v_{\max}$ is constant, to make $a_{\max}$ four times, $ω$ should be made four times.
From (1), A should be made one-fourth.

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