Question

A simple pendulum 4m long swings with an amplitude of 0.2m. Compute the velocity of the pendulum at its lowest point and it's acceleration at extreme ends.

Answer 1

Answer:-

L = Length of pendulum = 4m

Amplitude (r)  = 0.2 m

Time period of simple pendulum is given by = 2$\pi$ √(l/g) = 2$\pi$ √4/10 = 3.97 sec (Taking g = 10 here).

i) Velocity of the pendulum at its lowest point

V = Ψ √(r² - y²) .... (1)

At lowest point, y= 0

r = 0.2 , Ψ = 2$\pi$/T = 2$\pi$/3.97

Substituting above in (1) we get,

V = 0.32 m/s

ii) Acceleration at extreme ends

a = Ψ² y ...(2)

Here y = 0.2,   Ψ = 2$\pi$/T = 2$\pi$/3.97

Substituting above in (2) we get,

a = 0.5 m/s²