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
1.7 kgk = ?22.5 cm

Hanging a 1.7 kg mass on a spring stretches it by 22.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.7 kgx = 22.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2 kgk = ?9 cm

Hanging a 2 kg mass on a spring stretches it by 9 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2 kgx = 9 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.6 mT = 4.13 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 4.13 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 4.13 s
g = m/s²
5.Hard
1.3 kgk = 400 N/mA = 17 cm

A 1.3 kg mass on a spring with k = 400 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.3 kgk = 400 N/mA = 17 cm
amax = m/s²
6.Hard
3.9 kgk = 70 N/mA = 17 cm

A 3.9 kg mass on a spring with k = 70 N/m is pulled 17 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.9 kgk = 70 N/mA = 17 cm
vmax = m/s

Answer key

  1. 1. k = 74.12 N/m
  2. 2. k = 218 N/m
  3. 3. L = 1.948 m
  4. 4. g = 3.703 m/s²
  5. 5. amax = 52.31 m/s²
  6. 6. vmax = 0.7202 m/s

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