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
3.1 kgk = 60 N/m

A 3.1 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the period T.

m = 3.1 kgk = 60 N/m
T = s
2.Easy
3.9 kgk = 200 N/m

A 3.9 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 200 N/m
T = s
3.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.65 s

A 3.1 kg mass on a spring with k = 200 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.65 s (with sign).

m = 3.1 kgk = 200 N/mA = 14 cmt = 0.65 s
x = cm
5.Hard
t (s)x (cm)t = ?4.5

A body oscillates in simple harmonic motion with period 1.8 s and amplitude 18 cm. What is the shortest time t it needs to move from its maximum displacement of 18 cm to a displacement of 4.5 cm?

T = 1.8 sA = 18 cmx = 4.5 cm
t = s
6.Hard
3.6 kgk = 150 N/mA = 17 cm

A 3.6 kg mass on a spring with k = 150 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.6 kgk = 150 N/mA = 17 cm
E = J

Answer key

  1. 1. T = 1.428 s
  2. 2. T = 0.8774 s
  3. 3. T = 2.691 s
  4. 4. x = 6.817 cm
  5. 5. t = 0.3776 s
  6. 6. E = 2.168 J

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