First slide

Simple harmonic motion

Question

A body executing SHM has a maximum velocity 1 m/sec, maximum acceleration of 4 m/ $s e c^{2}$ . It’s amplitude in meters is

Moderate

A

1
B

0.75
C

0.5
D

0.25

Solution

Given $v_{\max} = 1 m/s$
$v_{max} = 1 m / s^{2} = ω A - - - (1) . h e r e ω i s a n g u l a r v e l o c i t y, A i s a m p l i t u d e a_{max} {=4m/s}^{2} {=-ω}^{2} A---(2) s q u a r i n g e q u a t i o n (1) \div e q u a t i o n (2) \frac{1}{4} = \frac{ω^{2} A^{2}}{ω^{2} A} \Rightarrow \frac{1}{4} = A = 0.25 m$

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