Procedure-4: Use Bounce of Module to measure the period with Timer and Masses setting in the table below. Attach m3= 250 g Attach m2= 100 g Attach m,= 50 g Mass Setting: Measure 10 cycles of oscillations on timer as: At. Period: Δε
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![**Procedure 4: Using the Bounce of a Module to Measure Spring Oscillation Periods**
**Objective:** Measure the period of oscillation for different masses using a timer.
**Mass Settings:**
1. Attach mass \( m_1 = 50 \, \text{g} \)
2. Attach mass \( m_2 = 100 \, \text{g} \)
3. Attach mass \( m_3 = 250 \, \text{g} \)
**Experimental Steps:**
1. For each mass, measure the time for 10 cycles of oscillation using the timer (\(\Delta t\)).
2. Calculate the period \( t \) as:
\[
t = \frac{\Delta t}{10}
\]
3. Repeat the measurement three times to obtain \( t^1, t^2, t^3 \).
4. Calculate the experimental period \( T^{\text{Exp}} \) as:
\[
T^{\text{Exp}} = \frac{t^1 + t^2 + t^3}{3}
\]
**Recorded Measurements:**
For \( m_1 = 50 \, \text{g} \):
- \(\Delta t = 10.71 \text{ s}, t = 1.07 \text{ s}\)
- \( T^{\text{Exp}} = 1.07 \text{ s} \)
For \( m_2 = 100 \, \text{g} \):
- \(\Delta t = 1.94 \text{ s}, t = 0.194 \text{ s}\)
- \( T^{\text{Exp}} = 0.194 \text{ s} \)
For \( m_3 = 250 \, \text{g} \):
- \(\Delta t = 42.40 \text{ s}, t = 4.24 \text{ s}\)
- \( T^{\text{Exp}} = 0.170 \text{ s} \)
**Theoretical Calculations:**
The theoretical period \( T^{\text{Th}} \) is calculated as:
\[
T^{\text{Th}} = 2\pi \sqrt{\frac{m}{k}}
\]
Where \( k \) is the spring constant and \( m \) is the mass.
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