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
4.7 kgk = 40 N/m

A 4.7 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.7 kgk = 40 N/m
f = Hz
2.Easy
4.5 kgk = 360 N/m

A 4.5 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 4.5 kgk = 360 N/m
T = s
3.Medium
1.3 kgk = 270 N/mA = 14 cmx = 6 cm

A 1.3 kg mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its speed v when it is 6 cm from equilibrium.

m = 1.3 kgk = 270 N/mA = 14 cmx = 6 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
5.Hard
1.6 kgk = 320 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 320 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.6 kgk = 320 N/mg = 9.81 m/s²
xmax = cm
6.Hard
3.4 kgk = 210 N/mA = 11 cm

A 3.4 kg mass on a spring with k = 210 N/m is pulled 11 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.4 kgk = 210 N/mA = 11 cm
amax = m/s²

Answer key

  1. 1. f = 0.4643 Hz
  2. 2. T = 0.7025 s
  3. 3. v = 1.823 m/s
  4. 4. L = 0.159 m
  5. 5. xmax = 9.81 cm
  6. 6. amax = 6.794 m/s²

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