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
3.2 kgk = ?

A 3.2 kg mass on a spring makes 25 complete oscillations in 33 s. Find the spring stiffness k.

m = 3.2 kgN = 25t = 33 s
k = N/m
2.Easy
1.9 kgk = ?

A 1.9 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 1.9 kgT = 0.7 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.9 mT = 6.8 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 6.8 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 6.8 s
g = m/s²
5.Hard
1.8 kgk = 290 N/mA = 9 cm

A 1.8 kg mass on a spring with k = 290 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 290 N/mA = 9 cm
E = J
6.Hard
0.9 kgk = 410 N/mA = 13 cm

A 0.9 kg mass on a spring with k = 410 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.9 kgk = 410 N/mA = 13 cm
amax = m/s²

Answer key

  1. 1. k = 72.5 N/m
  2. 2. k = 153.1 N/m
  3. 3. L = 2.236 m
  4. 4. g = 1.622 m/s²
  5. 5. E = 1.174 J
  6. 6. amax = 59.22 m/s²

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