Question

A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (as shown in the following figure). Find the frequency of vibration of the system for small values of the amplitude (small ?). Assume that the vertical suspension of length L is rigid, but ignore its mass. (Use any variable or symbol stated above along with the following as necessary: g and ?.)
f =

A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (as shown in the following figure). Find the frequency of vibration of the system for small values of the amplitude (small ?). Assume that the vertical suspension of length L is rigid, but ignore its mass. (Use any variable or symbol stated above along with the following as necessary: g and ?.) f =

Answer 1

Answer 2

compression=theta*h

so,

balanciing torque,

mglsinx-k*(theta*h)*h=ml^2*alpha

or (mgl-kh^2)=mw^2

or w=((mgl-kh^2)/m)^0.5

so f=w/2pi

=(1/2pi)*((mgl-kh^2)/m)^0.5   

Answer 3

compression=theta*h

so,

balanciing torque,

mglsinx-k*(theta*h)*h=ml^2*alpha

or (mgl-kh^2)=mw^2

or w=((mgl-kh^2)/m)^0.5

so f=w/2pi

=(1/2pi)*((mgl-kh^2)/m)^0.5