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
3.3 kgk = ?

A 3.3 kg mass on a spring oscillates with a period of 0.6 s. Find the spring stiffness k.

m = 3.3 kgT = 0.6 s
k = N/m
2.Easy
0.5 kgk = ?21 cm

Hanging a 0.5 kg mass on a spring stretches it by 21 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.5 kgx = 21 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.1 s? Use g = 9.81 m/s². Find L.

T = 2.1 sg = 9.81 m/s²
L = m
4.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
5.Hard
2.7 kgk = 170 N/mA = 3 cm

A 2.7 kg mass on a spring with k = 170 N/m is pulled 3 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.7 kgk = 170 N/mA = 3 cm
vmax = m/s
6.Hard
1 kgk = 1800 N/m450 m/s

A 20 g bullet moving at 450 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 450 m/sM = 1 kgk = 1800 N/m
A = cm

Answer key

  1. 1. k = 361.9 N/m
  2. 2. k = 23.36 N/m
  3. 3. L = 1.096 m
  4. 4. T = 3.357 s
  5. 5. vmax = 0.238 m/s
  6. 6. A = 21 cm

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