A 80 kg person is on a playground swing, with a chain length of 3.0 m. They are

Question

A 80 kg person is on a playground swing, with a chain length of 3.0 m. They are swinging 1.0 m forward and back from their equilibrium position. (a) What are the period and frequency of their oscillation back and forth? (b) What is their maximum velocity?
A 80 kg person is on a playground swing, with a chain length of 3.0 m. They are swinging 1.0 m forward and back from their equilibrium position. (a) What are the period and frequency of their oscillation back and forth? (b) What is their maximum velocity?
A 80 kg person is on a playground swing, with a chain length of 3.0 m. They are swinging 1.0 m forward and back from their equilibrium position. (a) What are the period and frequency of their oscillation back and forth? (b) What is their maximum velocity?

Explanation / Answer

mass of person, m = 80 kg

chain length, l = 3m

horizontal distance form the equilibrium point, a = 1 m

a. for a pendulum

time period T = 2*pi*sqroot(l/g)

T = 2*pi*sqroot(3/9.81) = 3.474 s

frequemcy = 1/T = 0.2878 Hz

b. let angular ampliutude be phiO

then l*sin(phiO) = a

sin(phiO) = a/l = 1/3

phiO = 0.339 rad

maximum velocity = l*phiO*2*pi/T

Vmax = 1.843 m/s

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