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
4.1 kgk = 370 N/m

A 4.1 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 4.1 kgk = 370 N/m
T = s
2.Easy
0.5 kgk = 210 N/m

A 0.5 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 210 N/m
T = s
3.Medium
L = 0.7 mT = 2.73 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 2.73 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 2.73 s
g = m/s²
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?3.2

A body oscillates in simple harmonic motion with period 2.6 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 3.2 cm?

T = 2.6 sA = 8 cmx = 3.2 cm
t = s
6.Hard
mk = 230 N/mA = 6 cmx = 2 cm

A mass on a spring with k = 230 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 230 N/mA = 6 cmx = 2 cm
U = J

Answer key

  1. 1. T = 0.6614 s
  2. 2. T = 0.3066 s
  3. 3. g = 3.708 m/s²
  4. 4. T = 2.537 s
  5. 5. t = 0.1703 s
  6. 6. U = 0.046 J

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