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
1.4 kgk = ?

A 1.4 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 1.4 kgT = 1 s
k = N/m
2.Easy
0.3 kgk = 370 N/m

A 0.3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 0.3 kgk = 370 N/m
T = s
3.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
4.Medium
L = 1 m

A simple pendulum has a length of 1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1 mg = 9.81 m/s²
T = s
5.Hard
3.9 kgk = 280 N/mA = 6 cm

A 3.9 kg mass on a spring with k = 280 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.9 kgk = 280 N/mA = 6 cm
amax = m/s²
6.Hard
3 kgk = 1300 N/m450 m/s

A 15 g bullet moving at 450 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 = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 450 m/sM = 3 kgk = 1300 N/m
A = cm

Answer key

  1. 1. k = 55.27 N/m
  2. 2. T = 0.1789 s
  3. 3. T = 1.419 s
  4. 4. T = 2.006 s
  5. 5. amax = 4.308 m/s²
  6. 6. A = 10.78 cm

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