A body oscillates in SHM according to the equation (in SI unit), x = 5 cos (2πt + π4). Its instantaneous displacement at t = 1s is

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

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)

$\Rightarrow x = 5 \cos \frac{π}{4}$ $[∵ \cos (360 ° + θ) = \cos θ]$

$\Rightarrow x = 5 \times \frac{1}{\sqrt{2}} = \frac{5}{\sqrt{2}} m$

Related content

10 Best World Environment Day Poster Ideas for School Students

GK Questions on Right to Education

List of Singular and Plural Words in English Grammar with Rules

MBBS Fees for 5 Years in India 2025 – Govt/Private Fee Structure In Medical Colleges

77 Best Happy Journey Quotes for Safe Travels in 2025

Essay on Operation Sindoor in English for Students

GK Questions on Mock Drill 2025

World Environment Day 2025 Quotes

CBSE Multiplication Worksheet for Class 4

Employability Skills for Class 10 Students