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
2.1 kgk = ?

A 2.1 kg mass on a spring makes 25 complete oscillations in 40 s. Find the spring stiffness k.

m = 2.1 kgN = 25t = 40 s
k = N/m
2.Easy
3.7 kgk = 280 N/m

A 3.7 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 280 N/m
T = s
3.Medium
L = 1.7 m

A simple pendulum has a length of 1.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.7 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.25 s

A 3.8 kg mass on a spring with k = 50 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.25 s (with sign).

m = 3.8 kgk = 50 N/mA = 4 cmt = 1.25 s
v = m/s
5.Hard
0.5 kgk = 430 N/mA = 18 cm

A 0.5 kg mass on a spring with k = 430 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 430 N/mA = 18 cm
E = J
6.Hard
t (s)x (cm)t = ?1.25

A body oscillates in simple harmonic motion with period 1.7 s and amplitude 5 cm. What is the shortest time t it needs to move from its maximum displacement of 5 cm to a displacement of 1.25 cm?

T = 1.7 sA = 5 cmx = 1.25 cm
t = s

Answer key

  1. 1. k = 32.38 N/m
  2. 2. T = 0.7223 s
  3. 3. T = 2.616 s
  4. 4. v = 0.1428 m/s
  5. 5. E = 6.966 J
  6. 6. t = 0.3566 s

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