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
2.8 kgk

A 2.8 kg mass on a spring makes 20 complete oscillations in 42 s. Find the frequency f of the oscillation.

m = 2.8 kgN = 20t = 42 s
f = Hz
2.Easy
1.3 kgk = 340 N/m

A 1.3 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 340 N/m
T = s
3.Medium
L = 1.5 mT = 2.3 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 2.3 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 2.3 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
3.6 kgk = 450 N/mA = 13 cm

A 3.6 kg mass on a spring with k = 450 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 450 N/mA = 13 cm
amax = m/s²
6.Hard
3.6 kgk = 300 N/mA = 18 cm

A 3.6 kg mass on a spring with k = 300 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.6 kgk = 300 N/mA = 18 cm
E = J

Answer key

  1. 1. f = 0.4762 Hz
  2. 2. T = 0.3885 s
  3. 3. g = 11.19 m/s²
  4. 4. L = 0.897 m
  5. 5. amax = 16.25 m/s²
  6. 6. E = 4.86 J

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