Home
Class 11
PHYSICS
Show that the equation x=acos^(2)omegat ...

Show that the equation `x=acos^(2)omegat` represents a simple harmonic motion. Find the (i) amplitude, (ii) time period and (iii) position of equilibrium of the particle.

Text Solution

Verified by Experts

`x=acos^(2)omegat=1/2a*2cos^(2)omegat=1/2a(cos2omegat+1)`
= `a/2+a/2cos2omegat`
The term `a/2cos2omegat` indicates simple harmonic motion.
(i) Amplitude = `1/2a`
(ii) Here, `omega.=2omega`
So, time period, `T=(2pi)/(omega.)=(2pi)/(2omega)=pi/omega`
(iii) Foe the term `a/2cos2omegat` simple harmonic motion,
acceleration = `-omega.^(2)x.=-4omega^(2)x." "[becauseomega.=2omega]`
At equilibrium position, acceleration = 0
`therefore" "0=-4omega^(2)x.or,x.=0`
As, `x=a/2+a/2cos2omegat=a/2+x.`
so, equlibrium position is,
`x=a/2+0or,x=a/2`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    CHHAYA PUBLICATION|Exercise WBJEE|5 Videos

  • SIMPLE HARMONIC MOTION

    CHHAYA PUBLICATION|Exercise JEE MAIN|6 Videos

  • SIMPLE HARMONIC MOTION

    CHHAYA PUBLICATION|Exercise INTEGER ANSWER TYPE|5 Videos

  • ROTATION OF RIGID BODIES

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|10 Videos

  • STATICS

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|3 Videos

Similar Questions

Explore conceptually related problems

Show that the equation x =acos^2omegat represents a simple harmonic motion. Find the:- amplitude.

Show that the equation x=Asinomegat represents a simple harmonic motion.

Show that the equation x=asinomegat+bcosomegat represents a simple harmonic motion.

Show that the equation x- a sin omegat + b cos omegat represents a simple harmonic motion.

If the equation x=asinomegat represents a simple harmonic motion of a particle, then its initial position is

Show that the equation x=Acos(omegat-alpha) is a mathematical representation of simple harmonic motion. Find the time period and the maximum speed of the motion.

Show that the equation x=Asin(omegat-alpha) is the mathematical representation of a simple harmonic motion. Find the time period and the maximum acceleration of the motion.

The equation x=(sint+cost) cm represents a simple harmonic motion along x-axis. Determine the amplitude, time period maximum velocity and maximum acceleration for the motion.

The equation x=(sqrt3sinpit+cospit) cm represents a simple harmonic motion x-axis. Determine the amplitude, time period, maximum velocity and maximum acceleration for the motion.

Equation of a simple harmonic motion is y=2sin(4t+pi/6) . Find out its period and initial phase.