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
1.9 kgk = ?

A 1.9 kg mass on a spring oscillates with a period of 2.5 s. Find the spring stiffness k.

m = 1.9 kgT = 2.5 s
k = N/m
2.Easy
3.3 kgk = 250 N/m

A 3.3 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 250 N/m
T = s
3.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
4.Medium
2.3 kgk = 230 N/mA = 11 cmx = 1 cm

A 2.3 kg mass on a spring with k = 230 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 1 cm from equilibrium.

m = 2.3 kgk = 230 N/mA = 11 cmx = 1 cm
v = m/s
5.Hard
1.5 kgk = 270 N/mA = 4 cm

A 1.5 kg mass on a spring with k = 270 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 270 N/mA = 4 cm
E = J
6.Hard
1 kgk = 210 N/m

A 1 kg mass is attached to the lower end of an unstretched vertical spring with k = 210 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1 kgk = 210 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. k = 12 N/m
  2. 2. T = 0.7219 s
  3. 3. L = 0.897 m
  4. 4. v = 1.095 m/s
  5. 5. E = 0.216 J
  6. 6. xmax = 9.343 cm

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