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
2.2 kgk = 10 N/m

A 2.2 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.2 kgk = 10 N/m
f = Hz
2.Easy
3.9 kgk = 300 N/m

A 3.9 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 300 N/m
T = s
3.Medium
L = 1 mT = 4.94 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 4.94 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 4.94 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
5.Hard
2.8 kgk = 80 N/mA = 17 cm

A 2.8 kg mass on a spring with k = 80 N/m is pulled 17 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.8 kgk = 80 N/mA = 17 cm
vmax = m/s
6.Hard
1.8 kgk = 370 N/mA = 6 cm

A 1.8 kg mass on a spring with k = 370 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.8 kgk = 370 N/mA = 6 cm
amax = m/s²

Answer key

  1. 1. f = 0.3393 Hz
  2. 2. T = 0.7164 s
  3. 3. g = 1.618 m/s²
  4. 4. L = 1.553 m
  5. 5. vmax = 0.9087 m/s
  6. 6. amax = 12.33 m/s²

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