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
1.8 kgk = ?

A 1.8 kg mass on a spring oscillates with a period of 2.2 s. Find the spring stiffness k.

m = 1.8 kgT = 2.2 s
k = N/m
2.Easy
0.7 kgk = ?

A 0.7 kg mass on a spring makes 30 complete oscillations in 46 s. Find the spring stiffness k.

m = 0.7 kgN = 30t = 46 s
k = N/m
3.Medium
0.5 kgk = 450 N/mA = 14 cmx = 7 cm

A 0.5 kg mass on a spring with k = 450 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 = 0.5 kgk = 450 N/mA = 14 cmx = 7 cm
v = m/s
4.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
5.Hard
1.5 kgk = 700 N/m100 m/s

A 5 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 = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 100 m/sM = 1.5 kgk = 700 N/m
A = cm
6.Hard
mk = 150 N/mA = 10 cmx = 1 cm

A mass on a spring with k = 150 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 150 N/mA = 10 cmx = 1 cm
K = J

Answer key

  1. 1. k = 14.68 N/m
  2. 2. k = 11.75 N/m
  3. 3. v = 3.637 m/s
  4. 4. T = 0.8971 s
  5. 5. A = 1.54 cm
  6. 6. K = 0.7425 J

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