A student measured 15s for the 20 complete oscillations for an object of 200g attached at the free end of a spring. Calculate the period of oscillation (T) and the spring constant (k).
My work (just wanted to ask for opinions if this is right):
T = 2π√(m/k)
T = 20 oscillation/15 seconds = 1.33 s for 1 oscillation
1.33 = 2π√(0.2 kg/k)
k = 0.0456 N/kg
T = 1.33, k = 0.0456 N/kg
Thanks in advance for any replies.
where did you get period as 1.33 seconds?
15sec/20=.75 sec= period
it is 1.33 oscillation per second...= frequency...
Your calculations and approach are almost correct, but there is a slight mistake in your final calculation of the spring constant.
Here's how you can calculate the period of oscillation (T) and the spring constant (k):
To find T, divide the total time by the number of oscillations:
T = (total time) / (number of oscillations)
In this case, the total time for 20 oscillations is given as 15 seconds:
T = 15 s / 20 = 0.75 s
So the period of oscillation is T = 0.75 s.
To find the spring constant (k), you can use the formula you mentioned:
T = 2π√(m/k)
Rearranging the formula to solve for k:
k = (4π²m) / T²
Where:
m = mass of the object = 0.2 kg
T = period of oscillation = 0.75 s
Now, plug in the values and calculate:
k = (4π² * 0.2 kg) / (0.75 s)²
k ≈ 1.68 N/m (rounded to two decimal places)
So the spring constant is k ≈ 1.68 N/m.
Therefore, the correct values are:
T = 0.75 s
k ≈ 1.68 N/m