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
3.3 kgk = 140 N/m

A 3.3 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 140 N/m
T = s
2.Easy
2.5 kgk = ?9 cm

Hanging a 2.5 kg mass on a spring stretches it by 9 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.5 kgx = 9 cmg = 9.81 m/s²
k = N/m
3.Medium
3.9 kgk = 170 N/mA = 7 cmx = 3 cm

A 3.9 kg mass on a spring with k = 170 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 3 cm from equilibrium.

m = 3.9 kgk = 170 N/mA = 7 cmx = 3 cm
v = m/s
4.Medium
3.7 kgk = 260 N/mA = 12 cmx = 1 cm

A 3.7 kg mass on a spring with k = 260 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 1 cm from equilibrium.

m = 3.7 kgk = 260 N/mA = 12 cmx = 1 cm
v = m/s
5.Hard
mk = 40 N/mA = 17 cmx = 13 cm

A mass on a spring with k = 40 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its kinetic energy K when it is 13 cm from equilibrium.

k = 40 N/mA = 17 cmx = 13 cm
K = J
6.Hard
2.8 kgk = 260 N/m

A 2.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 260 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.8 kgk = 260 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.9647 s
  2. 2. k = 272.5 N/m
  3. 3. v = 0.4176 m/s
  4. 4. v = 1.002 m/s
  5. 5. K = 0.24 J
  6. 6. xmax = 21.13 cm

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