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
4.2 kgk = 340 N/m

A 4.2 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 4.2 kgk = 340 N/m
T = s
2.Easy
1.8 kgk

A 1.8 kg mass on a spring makes 20 complete oscillations in 53 s. Find the frequency f of the oscillation.

m = 1.8 kgN = 20t = 53 s
f = Hz
3.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
5.Hard
1.7 kgk = 500 N/mA = 13 cm

A 1.7 kg mass on a spring with k = 500 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.7 kgk = 500 N/mA = 13 cm
amax = m/s²
6.Hard
2.5 kgk = 490 N/mA = 5 cm

A 2.5 kg mass on a spring with k = 490 N/m is pulled 5 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 490 N/mA = 5 cm
vmax = m/s

Answer key

  1. 1. T = 0.6983 s
  2. 2. f = 0.3774 Hz
  3. 3. T = 1.419 s
  4. 4. L = 0.159 m
  5. 5. amax = 38.24 m/s²
  6. 6. vmax = 0.7 m/s

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