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
1.8 kgk = 110 N/m

A 1.8 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 1.8 kgk = 110 N/m
T = s
2.Easy
3.5 kgk = 90 N/m

A 3.5 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 90 N/m
T = s
3.Medium
L = 2 mT = 2.66 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 2.66 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 2.66 s
g = m/s²
4.Medium
L = 1.4 m

A simple pendulum has a length of 1.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.4 mg = 9.81 m/s²
T = s
5.Hard
1 kgk = 300 N/m450 m/s

A 15 g bullet moving at 450 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 450 m/sM = 1 kgk = 300 N/m
A = cm
6.Hard
0.8 kgk = 430 N/mA = 16 cm

A 0.8 kg mass on a spring with k = 430 N/m is pulled 16 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.8 kgk = 430 N/mA = 16 cm
vmax = m/s

Answer key

  1. 1. T = 0.8037 s
  2. 2. T = 1.239 s
  3. 3. g = 11.16 m/s²
  4. 4. T = 2.374 s
  5. 5. A = 38.68 cm
  6. 6. vmax = 3.709 m/s

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