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
2.9 kgk

A 2.9 kg mass on a spring makes 25 complete oscillations in 53 s. Find the frequency f of the oscillation.

m = 2.9 kgN = 25t = 53 s
f = Hz
2.Easy
4.4 kgk = 140 N/m

A 4.4 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.4 kgk = 140 N/m
f = Hz
3.Medium
t (s)x (cm)1.5 s

A 3.5 kg mass on a spring with k = 350 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.5 s (with sign).

m = 3.5 kgk = 350 N/mA = 3 cmt = 1.5 s
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 210 N/mA = 16 cm

A 0.5 kg mass on a spring with k = 210 N/m is pulled 16 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.5 kgk = 210 N/mA = 16 cm
vmax = m/s
6.Hard
1.4 kgk = 100 N/mA = 9 cm

A 1.4 kg mass on a spring with k = 100 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.4 kgk = 100 N/mA = 9 cm
E = J

Answer key

  1. 1. f = 0.4717 Hz
  2. 2. f = 0.8978 Hz
  3. 3. v = −0.1951 m/s
  4. 4. L = 1.68 m
  5. 5. vmax = 3.279 m/s
  6. 6. E = 0.405 J

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