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
1.6 kgk = ?

A 1.6 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 1.6 kgT = 0.7 s
k = N/m
2.Easy
2.4 kgk = 240 N/m

A 2.4 kg mass on a spring with stiffness 240 N/m oscillates on a frictionless surface. Find the period T.

m = 2.4 kgk = 240 N/m
T = s
3.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
0.2 kgk = 460 N/mA = 20 cm

A 0.2 kg mass on a spring with k = 460 N/m is pulled 20 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 460 N/mA = 20 cm
E = J
6.Hard
t (s)x (cm)t = ?9.6

A body oscillates in simple harmonic motion with period 3.9 s and amplitude 12 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 9.6 cm?

T = 3.9 sA = 12 cmx = 9.6 cm
t = s

Answer key

  1. 1. k = 128.9 N/m
  2. 2. T = 0.6283 s
  3. 3. T = 2.537 s
  4. 4. L = 2.09 m
  5. 5. E = 9.2 J
  6. 6. t = 0.5756 s

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