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
0.4 kgk = ?16.5 cm

Hanging a 0.4 kg mass on a spring stretches it by 16.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.4 kgx = 16.5 cmg = 9.81 m/s²
k = N/m
2.Easy
1.4 kgk = ?

A 1.4 kg mass on a spring oscillates with a period of 1.65 s. Find the spring stiffness k.

m = 1.4 kgT = 1.65 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
5.Hard
3 kgk = 480 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 480 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 3 kgk = 480 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1.5 kgk = 2000 N/m100 m/s

A 20 g bullet moving at 100 m/s hits and stays in a 1.5 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 = 100 m/sM = 1.5 kgk = 2000 N/m
A = cm

Answer key

  1. 1. k = 23.78 N/m
  2. 2. k = 20.3 N/m
  3. 3. L = 1.315 m
  4. 4. T = 2.198 s
  5. 5. vmax = 0.7755 m/s
  6. 6. A = 3.627 cm

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