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
1.4 kgk = ?

A 1.4 kg mass on a spring makes 40 complete oscillations in 14 s. Find the spring stiffness k.

m = 1.4 kgN = 40t = 14 s
k = N/m
2.Easy
0.7 kgk = ?

A 0.7 kg mass on a spring makes 20 complete oscillations in 20 s. Find the spring stiffness k.

m = 0.7 kgN = 20t = 20 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.7 s? Use g = 9.81 m/s². Find L.

T = 1.7 sg = 9.81 m/s²
L = m
4.Medium
L = 2.1 m

A simple pendulum has a length of 2.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.1 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?12

A body oscillates in simple harmonic motion with period 1.4 s and amplitude 15 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12 cm?

T = 1.4 sA = 15 cmx = 12 cm
t = s
6.Hard
3 kgk = 100 N/m100 m/s

A 20 g bullet moving at 100 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 3 kgk = 100 N/m
A = cm

Answer key

  1. 1. k = 451.2 N/m
  2. 2. k = 27.63 N/m
  3. 3. L = 0.7181 m
  4. 4. T = 2.907 s
  5. 5. t = 0.2066 s
  6. 6. A = 11.51 cm

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