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
0.7 kgk = ?3 cm

Hanging a 0.7 kg mass on a spring stretches it by 3 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.7 kgx = 3 cmg = 9.81 m/s²
k = N/m
2.Easy
4.1 kgk = 150 N/m

A 4.1 kg mass on a spring with stiffness 150 N/m oscillates on a frictionless surface. Find the period T.

m = 4.1 kgk = 150 N/m
T = s
3.Medium
L = 2.9 m

A simple pendulum has a length of 2.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.9 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?12.75

A body oscillates in simple harmonic motion with period 0.5 s and amplitude 17 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12.75 cm?

T = 0.5 sA = 17 cmx = 12.75 cm
t = s
6.Hard
0.9 kgk = 470 N/m

A 0.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 470 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.9 kgk = 470 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 228.9 N/m
  2. 2. T = 1.039 s
  3. 3. T = 3.416 s
  4. 4. L = 0.3007 m
  5. 5. t = 0.06749 s
  6. 6. vmax = 0.4293 m/s

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