First slide

Simple harmonic motion

Question

A body oscillates with S.H.M according to the equation $x=5cos [2πt+ \frac{π}{4}]$ metre its instantaneous displacement at t=1 sec is

Moderate

A

$\frac{\sqrt{2}}{5} m$
B

$\frac{1}{\sqrt{3}} m$
C

$\frac{1}{\sqrt{2}} m$
D

$\frac{5}{\sqrt{2}} m$

Solution

Given $x=5cos [2πt+ \frac{π}{4}]$ where x is a displacement, t is time
=> $x=5cos [2 π+π / 4]$ at t=1 second
=> $x=5cos π /4$ as $[\cos (360^{\circ} + θ) =cosθ]$
=>x=5( $\frac{1}{\sqrt{2}}$ ) meter

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