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
4.4 kgk = 340 N/m

A 4.4 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 4.4 kgk = 340 N/m
T = s
2.Easy
2 kgk = 280 N/m

A 2 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2 kgk = 280 N/m
f = Hz
3.Medium
L = 0.8 mT = 4.42 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 4.42 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 4.42 s
g = m/s²
4.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
5.Hard
3.3 kgk = 320 N/mA = 11 cm

A 3.3 kg mass on a spring with k = 320 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.3 kgk = 320 N/mA = 11 cm
E = J
6.Hard
1.4 kgk = 500 N/m

A 1.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 500 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.4 kgk = 500 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.7148 s
  2. 2. f = 1.883 Hz
  3. 3. g = 1.617 m/s²
  4. 4. T = 2.104 s
  5. 5. E = 1.936 J
  6. 6. vmax = 0.5191 m/s

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