pendulum oscillates is started with an amplitude of 0o = 5.0°. Its e(t) graph is shown at the top of the figure below. the same pendulum is started at an amplitude of 80 = 10.0°, which curve best describes the motion of the pendulum?
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.
![**Pendulum Oscillation Analysis**
A pendulum oscillates with an initial amplitude of \(\theta_0 = 5.0^\circ\). The graph depicting its angle \(\theta(t)\) is shown in the top figure below.
**Question:**
If the same pendulum is started at an amplitude of \(\theta_0 = 10.0^\circ\), which curve best describes the motion of the pendulum?
**Graphs Description:**
1. **Original Oscillation (Top Graph):**
- This graph shows the original pendulum oscillation with an amplitude of \(\theta_0 = 5.0^\circ\).
- The curve is a simple sinusoidal wave, oscillating between approximately \(+5\) and \(-5\).
2. **Comparison Graphs:**
- In the middle left graph (a and b):
- Curve (a) is magenta, with increased amplitude and altered frequency.
- Curve (b) is teal, showing a moderate change in amplitude and frequency compared to the original.
- In the middle right graph (c and d):
- Curve (c) is blue, slightly similar in shape to the original wave but with larger amplitude.
- Curve (d) is orange, with a larger amplitude and a different frequency.
- In the bottom graph (e and f):
- Curve (e) is red, closely resembling the original waveform but expanded in amplitude.
- Curve (f) is blue and dashed with a noticeable increase in amplitude and slight frequency alteration.
**Choice Options:**
- (a)
- (b)
- (c)
- (d)
- (e)
- (f)
**Task:** Determine which curve, among (a) to (f), best represents the pendulum's motion at \(\theta_0 = 10.0^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0fdd9be-9990-44a9-8005-60989cbb2f12%2Fe24e4fd7-7a9b-4afe-824b-aa1c3134c723%2Fq40vlgw_processed.png&w=3840&q=75)
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