Various Formulae of S H M

             S.H.M. of a liquid in U tube

If a liquid of density r contained in a vertical U tube performs S.H.M. in its two limbs. Then time period

where  L = Total length of liquid column,h = Height of undisturbed liquid in each limb (L=2h)

 
 

S.H.M. of a bar magnet in a magnetic field
                                            

   

 

 

I = Moment of inertia of magnet

M = Magnetic moment of magnet

B = Magnetic field intensity

S.H.M. of a floating cylinder If l is the length of cylinder dipping in liquid then time period

S.H.M. of ball in the neck of an air chamber

m = mass of the ball

V = volume of air- chamber

A = area of cross section of neck

E = Bulk modulus for Air     

 
S.H.M. of a small ball rolling down in

hemi-spherical bowl

R = radius of the bowl

r  =radius of the ball

S.H.M. of a body suspended from a wire

 

S.H.M. of a piston in a cylinder

M = mass of the piston

A = area of cross section

h = height of cylinder

P = pressure in a cylinder

S.H.M of a cubical block

M = mass of the block

L = length of side of cube

h = modulus of rigidity

S.H.M. of a body in a tunnel dug along any chord of earth

= 84.6  minutes
 

S.H.M. of body in the tunnel dug along the diameter of earth

S.H.M. of   a conical pendulum

L = length of string

q = angle of string from the vertical

g = acceleration due to gravity

S.H.M. of L-C circuit

L = coefficient of self inductance

 C = capacity of condenser

 

 

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11    PMT    Physics    Oscillations    Various Formulae of S H M