A comprehensive review of simple harmonic motion, covering oscillation, period, frequency, and interpreting position vs. time graphs. Includes guided notes, practice problems, and a summative quiz.
In a perfect vacuum, an oscillator would move forever. However, in the real world, systems lose energy due to friction or air resistance. This process is called damping. Damping gradually reduces the amplitude of the motion until the system eventually comes to rest at equilibrium.
Key Takeaways
SHM requires a restoring force directed toward equilibrium.
"In Phase" means peaking at the same time.
Velocity is maximum as the object passes equilibrium.
Pendulum period depends only on length and gravity.
Reading Comprehension Questions
A. According to the text, what two conditions are required for a system to exhibit Simple Harmonic Motion?
B. Explain the difference between two oscillators that are "in phase" versus two that are "180 degrees out of phase."
C. Why does an object in SHM move past the equilibrium position instead of stopping there?
Part 3: 15 Practice Problems
Use Graph A below for questions 1–3.
12 cm
0
0.5 s
1.0 s
Pos
Time
Amplitude (Graph A):
Period (Graph A):
Frequency (Graph A):
A vibrating string moves 6 cm from equilibrium to its peak. What is its amplitude?
A pendulum takes 0.75 seconds to swing from its highest point on one side to the equilibrium position. Calculate the period.
A heartbeat is 80 beats per minute. Calculate the frequency in Hertz.
An oscillator completes 120 cycles in 3 minutes. What is its period in seconds?
If an object in SHM has an amplitude of 0.25 m, what is the total distance it travels in one complete cycle?
Use Graph B below for questions 9–11.
-5 m
12 s
24 s
Pos
Time
Amplitude (Graph B):
Period (Graph B):
Frequency (Graph B):
A tuning fork vibrates at 512 Hz. What is the period of one vibration?
A pendulum moves between +20 cm and -20 cm. What is its amplitude?
An object has a period of 0.5 seconds. How many cycles does it complete in 2 minutes?
On a position-time graph, peaks occur at \(t = 3 \text{s}\) and \(t = 9 \text{s}\). What is the frequency?
Part 4: 20 Multiple Choice
Use the comparison graph below for questions 1–3.
Wave A
Wave B
1. Which wave has the larger amplitude?
(A) Wave A
(B) Wave B
2. Which wave has the longer period?
(A) Wave A
(B) Wave B
3. Which wave has the higher frequency?
(A) Wave A
(B) Wave B
4. Where is the velocity of a pendulum zero?
(A) Equilibrium
(B) Max Displacement
(C) Halfway point
(D) Always constant
5. Two oscillators reaching peaks at the same time are:
(A) In Phase
(B) Out of Phase
(C) Non-harmonic
(D) Damped
6. One complete back-and-forth motion is called a:
(A) Cycle
(B) Wavelength
(C) Frequency
(D) Trough
7. Increasing pendulum length will ________ the period.
(A) Increase
(B) Decrease
(C) Not change
(D) Halve
8. Hertz is equal to:
(A) s per cycle
(B) cycles per s
(C) meters per s
(D) joules
9. Kinetic energy is maximum at:
(A) Max Displacement
(B) Equilibrium
(C) Turning point
(D) Zero velocity point
10. Amplitude reduction over time is called:
(A) Period
(B) Damping
(C) Phase
(D) Oscillation
Use the phase graph below for questions 11–12.
11. The two oscillators shown above are:
(A) In Phase
(B) 180 degrees Out of Phase
(C) Moving at different frequencies
(D) Perfectly synchronized
12. When the solid line oscillator is at its peak, the dashed line is at:
(A) Its peak
(B) Its trough
(C) Equilibrium
(D) Max velocity
13. A crest on a position-time graph is:
(A) Max positive pos
(B) Max negative pos
(C) Equilibrium
(D) Min displacement
14. Period is independent of ________ for a pendulum.
