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.,

d^{2}x

+

k

x = 0



dt^{2}

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)







7.


Initial phase is a (also called epoch)
i)

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

ii)

a =

p^{c}

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 = n_{max} = Aw when x = 0





10.


Acceleration, a = w^{2}x = Aw^{2} sin (wt + a)





11.


Maximum acceleration = w^{2}A when x = A





12.


P.E. of a particle performing S.H.M.,
P.E. = mw^{2}x^{2} = kx^{2}





13.


K.E. of a particle performing S.H.M., K.E. = mw^{2} (A^{2}
 x^{2}) = k (A^{2}  x^{2})





14.


Total energy of a particle in S.H.M,
E = mw^{2}A^{2}
= kA^{2}





15.


Composition of two SHMs,
x_{1} = A sin (wt + a) and x_{2} = 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


p^{2}






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.,
d^{2}x

+

k

q = 0.



dt^{2}

I





