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
2.1 kgk = 260 N/m

A 2.1 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 260 N/m
T = s
2.Easy
0.3 kgk

A 0.3 kg mass on a spring makes 20 complete oscillations in 50 s. Find the frequency f of the oscillation.

m = 0.3 kgN = 20t = 50 s
f = Hz
3.Medium
L = 0.9 mT = 1.2 s

An astronaut on another planet finds that a simple pendulum 0.9 m long has a period of 1.2 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.9 mT = 1.2 s
g = m/s²
4.Medium
t (s)x (cm)0.85 s

A 1.4 kg mass on a spring with k = 40 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.85 s (with sign).

m = 1.4 kgk = 40 N/mA = 4 cmt = 0.85 s
v = m/s
5.Hard
2.1 kgk = 100 N/m

A 2.1 kg mass is attached to the lower end of an unstretched vertical spring with k = 100 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.1 kgk = 100 N/mg = 9.81 m/s²
xmax = cm
6.Hard
4 kgk = 700 N/m100 m/s

An 8 g bullet moving at 100 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 100 m/sM = 4 kgk = 700 N/m
A = cm

Answer key

  1. 1. T = 0.5647 s
  2. 2. f = 0.4 Hz
  3. 3. g = 24.67 m/s²
  4. 4. v = 0.2108 m/s
  5. 5. xmax = 41.2 cm
  6. 6. A = 1.51 cm

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