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
2.1 kgk = 250 N/m

A 2.1 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.1 kgk = 250 N/m
f = Hz
2.Easy
2.2 kgk16 cm

Hanging a 2.2 kg mass on a spring stretches it by 16 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.2 kgx = 16 cmg = 9.81 m/s²
T = s
3.Medium
t (s)x (cm)1.3 s

A 2 kg mass on a spring with k = 170 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.3 s (with sign).

m = 2 kgk = 170 N/mA = 3 cmt = 1.3 s
x = cm
4.Medium
t (s)x (cm)0.65 s

A 2.3 kg mass on a spring with k = 300 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.65 s (with sign).

m = 2.3 kgk = 300 N/mA = 10 cmt = 0.65 s
x = cm
5.Hard
0.6 kgk = 410 N/mA = 20 cm

A 0.6 kg mass on a spring with k = 410 N/m is pulled 20 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.6 kgk = 410 N/mA = 20 cm
E = J
6.Hard
0.3 kgk = 70 N/m

A 0.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 70 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.3 kgk = 70 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. f = 1.737 Hz
  2. 2. T = 0.8024 s
  3. 3. x = 2.508 cm
  4. 4. x = 4.173 cm
  5. 5. E = 8.2 J
  6. 6. vmax = 0.6422 m/s

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