Question

A second pendulum is taken in a carriage.Find period of oscillation of carriage move with acceleration 4m/s 2 vertically upward

Answer 1

A seconds pendulum is a pendulum whose time period is 2 seconds.

These seconds pendulum we're frequently used in the antique wall clocks.

We know that the formula for the time period of a simple pendulum is
2π*√l/g
where l is the length of the pendulum and g is the effective acceleration due to gravity.

So,
Since the pendulum is in a carriage which itself is accelerating upwards with 4 m/s^2
That means if we observe the pendulum from the frame of carriage and try to visualize the forces acting on Bob of pendulum
There will be the gravitational force mg and the psuedo force that'll be acting on the Bob in the downward direction
That means the tension in the string equals = mg+ma = m(g+a)

So the effective g here is g+a= 14 m/s^2

Thus the time period will now become
2π√l/14 = 2π√1/14 and can be further calculated

The length of string of a seconds pendulum is 1.004 m when we consider the gravitational acceleration to be accurate as 9.81 m/s^2
However for our sake of convenience we have considered g = 10m/s^2 throughout the problem so we'll keep the value of l=1 metre.