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 = 270 N/m

A 0.8 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 270 N/m
T = s
2.Easy
3.2 kgk

A 3.2 kg mass on a spring makes 15 complete oscillations in 22 s. Find the frequency f of the oscillation.

m = 3.2 kgN = 15t = 22 s
f = Hz
3.Medium
L = 1.5 mT = 1.55 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 1.55 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 1.55 s
g = m/s²
4.Medium
3.7 kgk = 480 N/mA = 20 cmx = 2 cm

A 3.7 kg mass on a spring with k = 480 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 2 cm from equilibrium.

m = 3.7 kgk = 480 N/mA = 20 cmx = 2 cm
v = m/s
5.Hard
2.9 kgk = 250 N/m

A 2.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 250 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.9 kgk = 250 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
2 kgk = 2000 N/m400 m/s

A 20 g bullet moving at 400 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 2000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 400 m/sM = 2 kgk = 2000 N/m
A = cm

Answer key

  1. 1. T = 0.342 s
  2. 2. f = 0.6818 Hz
  3. 3. g = 24.65 m/s²
  4. 4. v = 2.267 m/s
  5. 5. vmax = 1.057 m/s
  6. 6. A = 12.59 cm

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