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
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 0.2 kgT = 1.1 s
k = N/m
2.Easy
3.1 kgk = 380 N/m

A 3.1 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.1 kgk = 380 N/m
f = Hz
3.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
4.Medium
L = 1.1 mT = 1.32 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.32 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.32 s
g = m/s²
5.Hard
2.5 kgk = 310 N/mA = 14 cm

A 2.5 kg mass on a spring with k = 310 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 310 N/mA = 14 cm
vmax = m/s
6.Hard
0.4 kgk = 320 N/m

A 0.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 320 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.4 kgk = 320 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 6.525 N/m
  2. 2. f = 1.762 Hz
  3. 3. T = 3.108 s
  4. 4. g = 24.92 m/s²
  5. 5. vmax = 1.559 m/s
  6. 6. vmax = 0.3468 m/s

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