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
4.8 kgk = 230 N/m

A 4.8 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 230 N/m
T = s
2.Easy
1.7 kgk = 40 N/m

A 1.7 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 1.7 kgk = 40 N/m
T = s
3.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 300 N/m350 m/s

A 15 g bullet moving at 350 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 350 m/sM = 0.5 kgk = 300 N/m
A = cm
6.Hard
2.6 kgk = 430 N/m

A 2.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 430 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.6 kgk = 430 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.9077 s
  2. 2. T = 1.295 s
  3. 3. T = 3.357 s
  4. 4. L = 0.994 m
  5. 5. A = 42.24 cm
  6. 6. xmax = 11.86 cm

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