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
3.5 kgk = 60 N/m

A 3.5 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 60 N/m
T = s
2.Easy
1.7 kgk = ?14 cm

Hanging a 1.7 kg mass on a spring stretches it by 14 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.7 kgx = 14 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.3 m

A simple pendulum has a length of 1.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.3 mg = 9.81 m/s²
T = s
4.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
5.Hard
3.3 kgk = 120 N/mA = 8 cm

A 3.3 kg mass on a spring with k = 120 N/m is pulled 8 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.3 kgk = 120 N/mA = 8 cm
vmax = m/s
6.Hard
2.5 kgk = 800 N/m100 m/s

A 20 g bullet moving at 100 m/s hits and stays in a 2.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 2.5 kgk = 800 N/m
A = cm

Answer key

  1. 1. T = 1.518 s
  2. 2. k = 119.1 N/m
  3. 3. T = 2.287 s
  4. 4. L = 1.68 m
  5. 5. vmax = 0.4824 m/s
  6. 6. A = 4.454 cm

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