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
3.4 kgk = 120 N/m

A 3.4 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 3.4 kgk = 120 N/m
T = s
2.Easy
1.1 kgk = 130 N/m

A 1.1 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the period T.

m = 1.1 kgk = 130 N/m
T = s
3.Medium
L = 0.8 m

A simple pendulum has a length of 0.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.8 mg = 9.81 m/s²
T = s
4.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 2 s and amplitude 4 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 3 cm?

T = 2 sA = 4 cmx = 3 cm
t = s
6.Hard
mk = 170 N/mA = 11 cmx = 7 cm

A mass on a spring with k = 170 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find the energy U stored in the spring when the mass is 7 cm from equilibrium.

k = 170 N/mA = 11 cmx = 7 cm
U = J

Answer key

  1. 1. T = 1.058 s
  2. 2. T = 0.578 s
  3. 3. T = 1.794 s
  4. 4. T = 2.457 s
  5. 5. t = 0.2699 s
  6. 6. U = 0.4165 J

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