First slide

Simple hormonic motion

Question

A body oscillates in SHM according to the equation (in SI unit), $x = 5 \cos (2 πt + \frac{π}{4})$ . Its instantaneous displacement at t = 1s is

Easy

A

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

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

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

$\frac{1}{2} m$

Solution

Given, $x = 5 co s (2 π t + \frac{π}{4})$ (where, x is displacement)
$\Rightarrow x = 5 \cos (2 π + \frac{π}{4})$ (At t = 1s)
$\Rightarrow x = 5 \cos \frac{π}{4}$ $[∵ \cos (360 ° + θ) = \cos θ]$
$\Rightarrow x = 5 \times \frac{1}{\sqrt{2}} = \frac{5}{\sqrt{2}} m$

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