Question

A particle undergoes a simple harmonic motion, the acceleration of the particle at a distance of 1.5 m from the center of motion being 6 m / s², the time of oscillation in seconds is

1. 2.00
2. 4.00
3. 3.14
4. 6.28

Answer 1

Correct Answer - Option 3 : 3.14

Concept:

Simple harmonic motion:

it is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy

a= ω² x

\(\;\omega = \frac{{2\pi }}{T}\)

\(a = \frac{{4\pi x}}{{{T^2}}}\)

\(T = 2\pi \sqrt {\frac{x}{a}} \)

a= acceleration

x= distance

T= time period

ω = angular velocity 

\(T = 2\pi \sqrt {\frac{{1.5}}{6}} \)

T = 3.14 sec