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
0.3 kgk = 170 N/m

A 0.3 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.3 kgk = 170 N/m
f = Hz
2.Easy
2.3 kgk = ?

A 2.3 kg mass on a spring makes 10 complete oscillations in 17 s. Find the spring stiffness k.

m = 2.3 kgN = 10t = 17 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?7.7

A body oscillates in simple harmonic motion with period 1.7 s and amplitude 11 cm. What is the shortest time t it needs to move from its maximum displacement of 11 cm to a displacement of 7.7 cm?

T = 1.7 sA = 11 cmx = 7.7 cm
t = s
6.Hard
3 kgk = 90 N/mA = 19 cm

A 3 kg mass on a spring with k = 90 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3 kgk = 90 N/mA = 19 cm
E = J

Answer key

  1. 1. f = 3.789 Hz
  2. 2. k = 31.42 N/m
  3. 3. L = 2.236 m
  4. 4. T = 2.198 s
  5. 5. t = 0.2152 s
  6. 6. E = 1.625 J

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