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
1 kgk = 200 N/m

A 1 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 1 kgk = 200 N/m
T = s
2.Easy
2.1 kgk = ?19.5 cm

Hanging a 2.1 kg mass on a spring stretches it by 19.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.1 kgx = 19.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 0.7 mT = 2.73 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 2.73 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 2.73 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
1.3 kgk = 430 N/mA = 19 cm

A 1.3 kg mass on a spring with k = 430 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.3 kgk = 430 N/mA = 19 cm
E = J
6.Hard
0.8 kgk = 270 N/mA = 11 cm

A 0.8 kg mass on a spring with k = 270 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.8 kgk = 270 N/mA = 11 cm
E = J

Answer key

  1. 1. T = 0.4443 s
  2. 2. k = 105.6 N/m
  3. 3. g = 3.708 m/s²
  4. 4. L = 0.8051 m
  5. 5. E = 7.762 J
  6. 6. E = 1.633 J

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