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
0.8 kgk = ?1.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 1.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.8 kgx = 1.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3.6 kgk

A 3.6 kg mass on a spring makes 40 complete oscillations in 49 s. Find the frequency f of the oscillation.

m = 3.6 kgN = 40t = 49 s
f = Hz
3.Medium
L = 1.3 mT = 5.63 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 5.63 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 5.63 s
g = m/s²
4.Medium
L = 0.7 m

A simple pendulum has a length of 0.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.7 mg = 9.81 m/s²
T = s
5.Hard
3.4 kgk = 190 N/mA = 8 cm

A 3.4 kg mass on a spring with k = 190 N/m is pulled 8 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.4 kgk = 190 N/mA = 8 cm
vmax = m/s
6.Hard
2.8 kgk = 360 N/mA = 13 cm

A 2.8 kg mass on a spring with k = 360 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 360 N/mA = 13 cm
E = J

Answer key

  1. 1. k = 523.2 N/m
  2. 2. f = 0.8163 Hz
  3. 3. g = 1.619 m/s²
  4. 4. T = 1.678 s
  5. 5. vmax = 0.598 m/s
  6. 6. E = 3.042 J

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