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 kgk = ?22.5 cm

Hanging a 3 kg mass on a spring stretches it by 22.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 3 kgx = 22.5 cmg = 9.81 m/s²
k = N/m
2.Easy
0.9 kgk = 380 N/m

A 0.9 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 0.9 kgk = 380 N/m
T = s
3.Medium
L = 1.6 mT = 1.6 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 1.6 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 1.6 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
3.3 kgk = 390 N/mA = 10 cm

A 3.3 kg mass on a spring with k = 390 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.3 kgk = 390 N/mA = 10 cm
vmax = m/s
6.Hard
1.5 kgk = 320 N/mA = 9 cm

A 1.5 kg mass on a spring with k = 320 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 320 N/mA = 9 cm
E = J

Answer key

  1. 1. k = 130.8 N/m
  2. 2. T = 0.3058 s
  3. 3. g = 24.67 m/s²
  4. 4. L = 0.897 m
  5. 5. vmax = 1.087 m/s
  6. 6. E = 1.296 J

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