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 = 90 N/m

A 2.8 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.8 kgk = 90 N/m
f = Hz
2.Easy
4.7 kgk = 100 N/m

A 4.7 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 100 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.7 s? Use g = 9.81 m/s². Find L.

T = 2.7 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.95 s

A 1.8 kg mass on a spring with k = 300 N/m is pulled 7 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.95 s (with sign).

m = 1.8 kgk = 300 N/mA = 7 cmt = 0.95 s
x = cm
5.Hard
2.6 kgk = 380 N/mA = 10 cm

A 2.6 kg mass on a spring with k = 380 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.6 kgk = 380 N/mA = 10 cm
vmax = m/s
6.Hard
0.7 kgk = 400 N/mA = 9 cm

A 0.7 kg mass on a spring with k = 400 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 400 N/mA = 9 cm
E = J

Answer key

  1. 1. f = 0.9023 Hz
  2. 2. T = 1.362 s
  3. 3. L = 1.811 m
  4. 4. x = 6.683 cm
  5. 5. vmax = 1.209 m/s
  6. 6. E = 1.62 J

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