MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Simple Harmonic Motion Formulae Page 1

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1.

 Equation of S.H.M., F = -kx where F is the restoring force, k is the force constant and x is the displacement.

2.

 Differential equation of S.H.M., d2x + k x = 0 dt2 m

Where m is the mass of the particle and k is the force constant.

3.

 Angular frequency, w = = 2p = 2pn, where n is the frequency. T

4.

 Time period, T = 2p

5.

 Displacement in SHM, x = A sin (wt + a)

6.

 Phase angle, is (wt + a)

7.

Initial phase is a (also called epoch)

i)

a = 0 for a particle starting from the mean position.

ii)

 a = pc for a particle starting from the extreme position. 2

8.

 Velocity of a particle performing linear S.H.M. = n = ±w= Aw cos (wt + a)

9.

 Maximum velocity = nmax = Aw when x = 0

10.

 Acceleration, a = -w2x = -Aw2 sin (wt + a)

11.

 Maximum acceleration = w2A when x = A

12.

 P.E. of a particle performing S.H.M., P.E. = mw2x2 = kx2

13.

 K.E. of a particle performing S.H.M., K.E. = mw2 (A2 - x2) = k (A2 - x2)

14.

 Total energy of a particle in S.H.M, E = mw2A2 = kA2

15.

Composition of two SHMs,
x1 = A sin (wt + a) and x2 = B sin (wt + b)
Resultant motion,
x = C sin (wt + d)
where C =

 And d = tan-1 [ A sin a + B sin b ] A cos a + B cos b

16.

 Period of simple pendulum, T = 2p l is the length of the pendulum.

17.

For a seconds pendulum, T = 2 seconds

 l = g p2

18.

 For a magnetic dipole in a uniform magnetic field, B T = 2p where I is the moment of inertia and M is the magnetic dipole moment.

19.

Differential equation of a body in angular S.H.M.,

 d2x + k q = 0. dt2 I

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