First slide

Simple hormonic motion

Question

The speed of a particle executing SHM is given by the equation $v^{2} = 144 - 9 x^{2}$ then the wrong statements among the following is

Moderate

A

Amplitude of the particle is 4 units
B

Time period is $\frac{π}{3}$ units
C

Maximum velocity is 12 units
D

Maximum acceleration is 36 units

Solution

maximum velocity in SHM is at x = 0 that is when there is no displacement.
Thus putting x = 0, the maximum velocity comes out to be = 12 units
$\begin{array}{l} V = \sqrt{144 - 9 x^{2}} \\ = 3 \sqrt{4^{2} - x^{2}} \end{array}$
Comparing with the equation $V = ω \sqrt{A^{2} - x^{2}}$ we get $ω = 3 and A = 4$
As a result T = $2 π / 3$
Also we know acceleration = $- ω^{2} x$ in the case of SHM
For maximum acceleration $x = A = 4$ which gives us maximum acceleration as 36 units,
Hence option 3 is wrong.

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