Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
0.8 kgk

A 0.8 kg mass on a spring makes 40 complete oscillations in 44 s. Find the frequency f of the oscillation.

m = 0.8 kgN = 40t = 44 s
f = Hz
2.Easy
3 kgk = 140 N/m

A 3 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the period T.

m = 3 kgk = 140 N/m
T = s
3.Medium
L = 1.9 mT = 2.91 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 2.91 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 2.91 s
g = m/s²
4.Medium
t (s)x (cm)1.05 s

A 2.6 kg mass on a spring with k = 130 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.05 s (with sign).

m = 2.6 kgk = 130 N/mA = 5 cmt = 1.05 s
x = cm
5.Hard
3.7 kgk = 180 N/mA = 7 cm

A 3.7 kg mass on a spring with k = 180 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 180 N/mA = 7 cm
vmax = m/s
6.Hard
0.1 kgk = 20 N/m

A 0.1 kg mass is attached to the lower end of an unstretched vertical spring with k = 20 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.1 kgk = 20 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 0.9091 Hz
  2. 2. T = 0.9198 s
  3. 3. g = 8.858 m/s²
  4. 4. x = 2.081 cm
  5. 5. vmax = 0.4882 m/s
  6. 6. xmax = 9.81 cm

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