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
0.9 kgk = 340 N/m

A 0.9 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 0.9 kgk = 340 N/m
T = s
2.Easy
4.1 kgk = 90 N/m

A 4.1 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 90 N/m
f = Hz
3.Medium
L = 1.6 mT = 4.13 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 4.13 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 4.13 s
g = m/s²
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?7

A body oscillates in simple harmonic motion with period 1.1 s and amplitude 14 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7 cm?

T = 1.1 sA = 14 cmx = 7 cm
t = s
6.Hard
1 kgk = 900 N/m100 m/s

An 8 g bullet moving at 100 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 = 900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 100 m/sM = 1 kgk = 900 N/m
A = cm

Answer key

  1. 1. T = 0.3233 s
  2. 2. f = 0.7457 Hz
  3. 3. g = 3.703 m/s²
  4. 4. T = 2.537 s
  5. 5. t = 0.09167 s
  6. 6. A = 2.656 cm

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