First slide

Simple hormonic motion

Question

A particle of mass 0.1 kg is executing simple harmonic motion with amplitude 20 cm along a straight line. Its maximum and minimum potential energies are 0.8 J and 0.6 J respectively. Then period of oscillation of the particle is

Easy

A

$\frac{π}{2} S$
B

$\frac{π}{4} S$
C

$\frac{π}{10} S$
D

$\frac{π}{5} S$

Solution

(4)
$E n e r g y o f o s c i l l a t i o n E = U_{\max} - U_{\min} = (0.8 - 0.6) J = 0.2 J$
$\begin{array}{l} ∴ \frac{1}{2} m ω^{2} A^{2} = E \Rightarrow ω = \frac{1}{A} \sqrt{\frac{2 E}{m}} \\ ∴ T = \frac{2 π}{ω} = 2 π . A \sqrt{\frac{m}{2 E}} = 2 π \times 0.2 \sqrt{\frac{0.1}{2 \times 0.2}} sec = \frac{π}{5} s e c . \end{array}$

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