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
4.9 kgk = 340 N/m

A 4.9 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 340 N/m
T = s
2.Easy
3.4 kgk = ?

A 3.4 kg mass on a spring makes 20 complete oscillations in 29 s. Find the spring stiffness k.

m = 3.4 kgN = 20t = 29 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.7 s? Use g = 9.81 m/s². Find L.

T = 1.7 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.7 s

A 3.7 kg mass on a spring with k = 180 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 = 0.7 s (with sign).

m = 3.7 kgk = 180 N/mA = 3 cmt = 0.7 s
x = cm
5.Hard
2.8 kgk = 370 N/mA = 13 cm

A 2.8 kg mass on a spring with k = 370 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 370 N/mA = 13 cm
E = J
6.Hard
0.3 kgk = 190 N/m

A 0.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 190 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.3 kgk = 190 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.7543 s
  2. 2. k = 63.84 N/m
  3. 3. L = 0.7181 m
  4. 4. x = 0.5076 cm
  5. 5. E = 3.127 J
  6. 6. vmax = 0.3898 m/s

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