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
1.5 kgk = ?4 cm

Hanging a 1.5 kg mass on a spring stretches it by 4 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.5 kgx = 4 cmg = 9.81 m/s²
k = N/m
2.Easy
3.4 kgk = ?

A 3.4 kg mass on a spring makes 20 complete oscillations in 13 s. Find the spring stiffness k.

m = 3.4 kgN = 20t = 13 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)1.4 s

A 2 kg mass on a spring with k = 100 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.4 s (with sign).

m = 2 kgk = 100 N/mA = 5 cmt = 1.4 s
x = cm
5.Hard
3.7 kgk = 310 N/mA = 7 cm

A 3.7 kg mass on a spring with k = 310 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.7 kgk = 310 N/mA = 7 cm
amax = m/s²
6.Hard
1 kgk = 470 N/mA = 9 cm

A 1 kg mass on a spring with k = 470 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1 kgk = 470 N/mA = 9 cm
E = J

Answer key

  1. 1. k = 367.9 N/m
  2. 2. k = 317.7 N/m
  3. 3. L = 1.315 m
  4. 4. x = −4.447 cm
  5. 5. amax = 5.865 m/s²
  6. 6. E = 1.903 J

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