Request a call back

derive expression for displacement in shm

when an object is subjected to a restoring force F that is proportional to displacement,

then the object is undergoing simple harmonic motion.

Let m be the mass of the object .

If restoring force F  is proportional to displacement x , then it is mathemetically written as

F ∝ x

F = - k x  ( negative sign is used because force is restoring force )

where k is proportionality constant and it is known as force constant

force F = mass × acceleration

Above expression can be written as

.........................(1)

where ω2 = k/m .

For above second order differential equation , the solution is written as

x = a cos(ωt) + b sin(ωt)  ......................(2)

where a and b are constants ,

If we choose the constants so that

a/b = tan φ ;  a =  A cos φ  ; b = A sin φ

then eqn.(2) will be written as

x = A [ cosφ  cos(ωt)+ sinφ sin(ωt)]

x = A cos( ωt - φ )

where A is amplitude , ω is angular frequency and φ is initial phase at t = 0

Answered by Thiyagarajan K | 02 Feb, 2024, 10:32: PM
CBSE 11-science - Physics
Asked by sy123946 | 07 Apr, 2024, 04:23: PM
CBSE 11-science - Physics
CBSE 11-science - Physics
CBSE 11-science - Physics
Asked by snehasahu824 | 03 Mar, 2020, 10:06: AM
CBSE 11-science - Physics
Asked by devvratagrahari | 02 Dec, 2019, 06:44: AM
CBSE 11-science - Physics
Asked by SELVA | 06 Jul, 2019, 03:25: PM