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
0.4 kgk = 30 N/m

A 0.4 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.4 kgk = 30 N/m
f = Hz
2.Easy
2.9 kgk = 340 N/m

A 2.9 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 2.9 kgk = 340 N/m
T = s
3.Medium
t (s)x (cm)0.1 s

A 3.6 kg mass on a spring with k = 110 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.1 s (with sign).

m = 3.6 kgk = 110 N/mA = 15 cmt = 0.1 s
x = cm
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
0.8 kgk = 170 N/m

A 0.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 170 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.8 kgk = 170 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
3.5 kgk = 190 N/mA = 18 cm

A 3.5 kg mass on a spring with k = 190 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 190 N/mA = 18 cm
amax = m/s²

Answer key

  1. 1. f = 1.378 Hz
  2. 2. T = 0.5803 s
  3. 3. x = 12.77 cm
  4. 4. L = 0.897 m
  5. 5. vmax = 0.673 m/s
  6. 6. amax = 9.771 m/s²

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