Question

Now, for parts G-I, you'll investigate what determines the frequency of oscillation. For these parts, turn off the friction using the slider bar.

Select the stopwatch, and time how long it takes for a weight to oscillate back and forth 10 times. The period of oscillation is this time divided by 10. The frequency of oscillation is one divided by the period.
How does the frequency of oscillation depend on the mass of the weight?

Answer 1

The frequency of oscillation does not depend on the mass of the weight in simple harmonic motion.

Step-by-step explanation:

The frequency of oscillation in a simple harmonic motion is determined by the properties of the system, specifically the stiffness of the spring and the mass attached to it. In the absence of friction, the mass of the weight does not alter the frequency of oscillation. The equation for the frequency of oscillation in a simple harmonic motion is:

`\[ \text{Frequency} (\text{f}) = \frac{1}{\text{Period} (\text{T})} \]`

Where the period T is the time taken for one complete oscillation. As per the instructions given, we measure the time taken for 10 oscillations and then divide it by 10 to obtain the period. Thus, the period T can be found as:

`\[ T = \frac{\text{Time for 10 oscillations}}{10} \]`

The frequency is inversely proportional to the period:

`\[ f = (1)/(T) \]`

So, regardless of the mass of the weight, when the system obeys simple harmonic motion and friction is not a factor, the frequency remains constant. This is a fundamental principle in simple harmonic motion where the restoring force is directly proportional to displacement, making the mass inconsequential in determining the frequency of oscillation. Therefore, altering the mass of the weight, within the constraints of simple harmonic motion, does not influence the frequency of oscillation.