Question

A spring with spring constant 13.0 N/m hangs from the ceiling. A 420 g ball is attached to the spring and allowed to come to rest. It is then pulled down 6.10 cm and released.

Part A

What is the time constant if the ball's amplitude has decreased to 4.00 cm after 43.0 oscillations?

Express your answer with the appropriate units.

Answer 1

period of oscillation T = 2 * pi * sqrt(mass / spring constant)

time taken to cover 43 oscillation t = 43 * T

t = 43 * 2 * pi * sqrt(m / k)

time constant TC = -t / ln(A(t) / A(0))

where,

A(t) = amplitude after time t

A(0) = initial amplitude

TC = (-43 * 2 * pi * sqrt(0.42 / 13)) / ln(4 / 6.1)

TC = 115.079 sec

time constant = 115.079 sec