Question

A pendulum is made of 75g mass connected to a 0.88 m strong, hanging from a support. The mass is pulled back 12 cm and released.

A) what is the position of the mass 30 seconds after it is released?

B) what is the maximum speed of mass?

Answer 1

we have,

mass of the pendulum

length of the pendulum

Amplitude of the pendulum distance by which the mass of pendulum is pulled back

acceleration due to gravity

Period of the pendulum will be given as,

using and   we get,

so, we get the frequency   of the pendulum as,

so, we get the angular frequency   of the pendulum as,

so the displacement of the pendulum as function of time   will be given as,

Using given and calculated in above equation we get,

_____________________________________ relation 1

differentiating above equation with respect to time   we get the velocity   of the pendulum as a function of time    as,

since speed is defined as the magnitude of velocity the speed   of the pendulum mass as a function of time is given as,

______________________________________ relation 2

A)

using time in relation 1 we get the position of pendulum mass after 30 s as,

So,

( expressed in two significant figures )

Here, positive sign indicates that the pendulum mass is at a distance of 11 cm away from the rest position on the same side as the side from where the pendulum mass was initially released.

B)

consider relation 2,

the pendulum will have maximum velocity when   becomes 1,

So, using   in relation 2 we get the maximum speed    of the pendulum mass as,

so, maximum speed of pendulum mass is,