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 kgk = 240 N/m

A 1 kg mass on a spring with stiffness 240 N/m oscillates on a frictionless surface. Find the period T.

m = 1 kgk = 240 N/m
T = s
2.Easy
3.8 kgk = 80 N/m

A 3.8 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.8 kgk = 80 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.5 s? Use g = 9.81 m/s². Find L.

T = 1.5 sg = 9.81 m/s²
L = m
4.Medium
L = 2 mT = 2.66 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 2.66 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 2.66 s
g = m/s²
5.Hard
0.7 kgk = 60 N/m

A 0.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 60 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.7 kgk = 60 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1 kgk = 600 N/m150 m/s

An 8 g bullet moving at 150 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 150 m/sM = 1 kgk = 600 N/m
A = cm

Answer key

  1. 1. T = 0.4056 s
  2. 2. f = 0.7303 Hz
  3. 3. L = 0.5591 m
  4. 4. g = 11.16 m/s²
  5. 5. vmax = 1.06 m/s
  6. 6. A = 4.88 cm

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