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
2.6 kgk = 270 N/m

A 2.6 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 2.6 kgk = 270 N/m
T = s
2.Easy
4.8 kgk = ?

A 4.8 kg mass on a spring oscillates with a period of 0.95 s. Find the spring stiffness k.

m = 4.8 kgT = 0.95 s
k = N/m
3.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
4.Medium
L = 1.4 mT = 5.84 s

An astronaut on another planet finds that a simple pendulum 1.4 m long has a period of 5.84 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.4 mT = 5.84 s
g = m/s²
5.Hard
2.9 kgk = 290 N/mA = 2 cm

A 2.9 kg mass on a spring with k = 290 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.9 kgk = 290 N/mA = 2 cm
E = J
6.Hard
2.7 kgk = 300 N/mA = 18 cm

A 2.7 kg mass on a spring with k = 300 N/m is pulled 18 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.7 kgk = 300 N/mA = 18 cm
vmax = m/s

Answer key

  1. 1. T = 0.6166 s
  2. 2. k = 210 N/m
  3. 3. g = 1.622 m/s²
  4. 4. g = 1.621 m/s²
  5. 5. E = 0.058 J
  6. 6. vmax = 1.897 m/s

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