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
0.4 kgk = ?24 cm

Hanging a 0.4 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.4 kgx = 24 cmg = 9.81 m/s²
k = N/m
2.Easy
2 kgk = ?

A 2 kg mass on a spring oscillates with a period of 1.75 s. Find the spring stiffness k.

m = 2 kgT = 1.75 s
k = N/m
3.Medium
L = 1 mT = 2.11 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 2.11 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 2.11 s
g = m/s²
4.Medium
0.2 kgk = 180 N/mA = 10 cmx = 1 cm

A 0.2 kg mass on a spring with k = 180 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 1 cm from equilibrium.

m = 0.2 kgk = 180 N/mA = 10 cmx = 1 cm
v = m/s
5.Hard
t (s)x (cm)t = ?8

A body oscillates in simple harmonic motion with period 2.7 s and amplitude 10 cm. What is the shortest time t it needs to move from its maximum displacement of 10 cm to a displacement of 8 cm?

T = 2.7 sA = 10 cmx = 8 cm
t = s
6.Hard
2 kgk = 1300 N/m150 m/s

A 15 g bullet moving at 150 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 150 m/sM = 2 kgk = 1300 N/m
A = cm

Answer key

  1. 1. k = 16.35 N/m
  2. 2. k = 25.78 N/m
  3. 3. g = 8.867 m/s²
  4. 4. v = 2.985 m/s
  5. 5. t = 0.2765 s
  6. 6. A = 4.396 cm

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