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
5 kgk = 250 N/m

A 5 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 250 N/m
T = s
2.Easy
1.8 kgk = ?12.5 cm

Hanging a 1.8 kg mass on a spring stretches it by 12.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.8 kgx = 12.5 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)1.5 s

A 3.3 kg mass on a spring with k = 150 N/m is pulled 7 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.5 s (with sign).

m = 3.3 kgk = 150 N/mA = 7 cmt = 1.5 s
v = m/s
4.Medium
3.4 kgk = 120 N/mA = 19 cmx = 8 cm

A 3.4 kg mass on a spring with k = 120 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 8 cm from equilibrium.

m = 3.4 kgk = 120 N/mA = 19 cmx = 8 cm
v = m/s
5.Hard
mk = 310 N/mA = 13 cmx = 1 cm

A mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 310 N/mA = 13 cmx = 1 cm
U = J
6.Hard
3 kgk = 1300 N/m100 m/s

A 20 g bullet moving at 100 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 = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 3 kgk = 1300 N/m
A = cm

Answer key

  1. 1. T = 0.8886 s
  2. 2. k = 141.3 N/m
  3. 3. v = 0.2998 m/s
  4. 4. v = 1.024 m/s
  5. 5. U = 0.0155 J
  6. 6. A = 3.192 cm

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