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
1.2 kgk = 250 N/m

A 1.2 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 1.2 kgk = 250 N/m
T = s
2.Easy
2.7 kgk = 180 N/m

A 2.7 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.7 kgk = 180 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
5.Hard
2 kgk = 310 N/m

A 2 kg mass is attached to the lower end of an unstretched vertical spring with k = 310 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2 kgk = 310 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1.5 kgk = 900 N/m250 m/s

A 12 g bullet moving at 250 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 250 m/sM = 1.5 kgk = 900 N/m
A = cm

Answer key

  1. 1. T = 0.4353 s
  2. 2. f = 1.299 Hz
  3. 3. L = 1.68 m
  4. 4. L = 0.2485 m
  5. 5. vmax = 0.788 m/s
  6. 6. A = 8.133 cm

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