Hooke’s Law and Simple Harmonic Motion

Simple Harmonic Motion
By Panun Bali
Aim: The aim of this experiment was to determine the spring constant “k” of a spring using Hooke’s Law and Simple Harmonic Motion.

Theory:

Part 1:
We know from the theory that the Time Period “T” for any spring that undergoes simple harmonic motion:

T = 2π * √ (m/k)

Where “T” is the Time Period of the spring; “m” is the mass attached to the spring and “k” is the spring constant of the spring used.

After mathematically manipulating the equation to make k the subject of the equation, we get:

T2/m = 4π2/k

As such the value of the spring constant, “k” is 4π2 divided by the gradient of a T2 against m graph (Grad1).

Part 2:
This investigation also uses Hooke’s Law to confirm the value. Hooke’s law states that F = kx. For this investigation, F is also equal to “mg”. Therefore:

kx = mg k = g(m/x) x/m = g/k
2
Where “k” is the spring constant, “g” is the acceleration due to gravity, “x” is the spring extension and “m” is the mass attached to the spring. This extension is determined by the difference in the extended length of the spring and it’s original length.

The “k” value is determined by dividing the “g” constant by the gradient of a graph where x (extension) is plotted against m (the mass attached) or Grad2.

Part 1 DCP

Raw Data Table:

Time Taken For 10 Oscillations/(s) ±0.01
Mass of Objects On String (M)/
(kg) ± 0.001
Trial 1
Trial 2
Trial 3
0.050
3.40
3.48
3.37
0.100
4.84
5.04
4.93
0.150
5.96
5.90
5.82
0.200
6.92
6.82
6.81
0.250
7.68
7.61
7.71
0.300
8.57
8.52
8.46
0.350
9.06
8.95
9.13

Mass Uncertainty
The masses used during the investigation were those manufactured by a factory and supplied to us. While weighing the masses, though the greatest deviation (from the indicated value) found for the masses was 1 gram. As such, this value was used for the error on the mass. Time Uncertainty
The error for time is both systematic and random. There is a