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
0.9 kgk = 350 N/m

A 0.9 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 0.9 kgk = 350 N/m
T = s
2.Easy
5 kgk = 270 N/m

A 5 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 270 N/m
T = s
3.Medium
2.5 kgk = 490 N/mA = 9 cmx = 7 cm

A 2.5 kg mass on a spring with k = 490 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 7 cm from equilibrium.

m = 2.5 kgk = 490 N/mA = 9 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
1.1 kgk = 160 N/mA = 8 cm

A 1.1 kg mass on a spring with k = 160 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.1 kgk = 160 N/mA = 8 cm
amax = m/s²
6.Hard
3 kgk = 700 N/m450 m/s

A 12 g bullet moving at 450 m/s hits and stays in a 3 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 = 12 gv = 450 m/sM = 3 kgk = 700 N/m
A = cm

Answer key

  1. 1. T = 0.3186 s
  2. 2. T = 0.855 s
  3. 3. v = 0.792 m/s
  4. 4. T = 0.8971 s
  5. 5. amax = 11.64 m/s²
  6. 6. A = 11.76 cm

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