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
3.7 kgk = ?

A 3.7 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 3.7 kgT = 1.1 s
k = N/m
2.Easy
1.6 kgk25 cm

Hanging a 1.6 kg mass on a spring stretches it by 25 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.6 kgx = 25 cmg = 9.81 m/s²
T = s
3.Medium
L = 0.8 mT = 2.92 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 2.92 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 2.92 s
g = m/s²
4.Medium
2.7 kgk = 390 N/mA = 14 cmx = 7 cm

A 2.7 kg mass on a spring with k = 390 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its speed v when it is 7 cm from equilibrium.

m = 2.7 kgk = 390 N/mA = 14 cmx = 7 cm
v = m/s
5.Hard
2.7 kgk = 200 N/m

A 2.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 200 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.7 kgk = 200 N/mg = 9.81 m/s²
xmax = cm
6.Hard
0.2 kgk = 100 N/m

A 0.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 100 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.2 kgk = 100 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 120.7 N/m
  2. 2. T = 1.003 s
  3. 3. g = 3.704 m/s²
  4. 4. v = 1.457 m/s
  5. 5. xmax = 26.49 cm
  6. 6. vmax = 0.4387 m/s

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