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 = 400 N/m

A 4.7 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 400 N/m
T = s
2.Easy
2.4 kgk = 340 N/m

A 2.4 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 2.4 kgk = 340 N/m
T = s
3.Medium
2.9 kgk = 140 N/mA = 13 cmx = 8 cm

A 2.9 kg mass on a spring with k = 140 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 8 cm from equilibrium.

m = 2.9 kgk = 140 N/mA = 13 cmx = 8 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
5.Hard
3 kgk = 1400 N/m200 m/s

A 5 g bullet moving at 200 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 200 m/sM = 3 kgk = 1400 N/m
A = cm
6.Hard
0.5 kgk = 1100 N/m300 m/s

A 20 g bullet moving at 300 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 300 m/sM = 0.5 kgk = 1100 N/m
A = cm

Answer key

  1. 1. T = 0.6811 s
  2. 2. T = 0.5279 s
  3. 3. v = 0.712 m/s
  4. 4. L = 0.6361 m
  5. 5. A = 1.542 cm
  6. 6. A = 25.09 cm

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