I have performed an experiment of simple harmonic motion and the values I got
Mass(g)Distance (m)
200 0.438
250 0.398
300 0.345
350 0.312
400 0.297
450 0.281
500 0.259
I would like to know how to calculate the spring constant... since I have been having weird values, if someone could please give me each value for k I will deeply appreciate it....
To calculate the spring constant (k) using the provided data, you'll need to apply Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law can be expressed as:
F = -kx
Where:
F is the force applied by the spring (in Newtons),
k is the spring constant (in Newtons per meter), and
x is the displacement from the equilibrium position (in meters).
In your experiment, the displacement (x) and mass (m) are given. To find the force, you can make use of Newton's second law:
F = mg
Where:
m is the mass (in kilograms) and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since you have the values of mass and displacement, you can calculate the force for each trial using the formula F = mg. Then, rearrange Hooke's Law to solve for k:
k = -F / x
By substituting the values of F and x into this equation, you can determine the spring constant (k) for each trial.
Here is the step-by-step calculation for the first data point (Mass = 200 g, Distance = 0.438 m):
Convert mass to kilograms:
m = 200 g = 200 / 1000 kg = 0.2 kg
Calculate force:
F = mg = 0.2 kg × 9.8 m/s^2 = 1.96 N
Calculate spring constant:
k = -F / x = -1.96 N / 0.438 m ≈ -4.47 N/m
Repeat this calculation for each data point to find the corresponding spring constant (k) for each trial.