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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 = 2
p 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 = 2
p
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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