Vocabulary: Mass on a Spring; Energy of SHM By Nick, Alex & Abish Pius Topics: Simple Harmonic Motion Topics: Mass on a Spring; Energy of SHM Motion of an Object Attached to a Spring

Damped Oscillations

Forced Oscillations Vocabulary: SHM oscillatory motion

simple harmonic motion

periodic motion

damped motion

forced motion

simple pendulum

mass on a spring

physical pendulum

torsion pendulum

displacement function

velocity function

acceleration function oscillatory motion

simple harmonic motion

periodic motion

damped motion

forced motion

mass on a spring

displacement function

velocity function

acceleration function

amplitude

time period Oscillatory Motion The Particle in Simple Harmonic Motion

Energy of the Simple Harmonic Oscillator

Comparing SHM and UCM Ex. A clown is rocking on a rocking chair in the dark. His glowing red nose moves back and forth a distance of 0.42 m exactly 30 times a MINUTE, in a simple harmonic motion.

1. What is the period of motion? T= total time/ #revs ANS. 2 sec/wave

2. What is the Frequency? F = 1/T Ans. .5Hz Ex. A 5.00 kg block hung on a spring causes a 10.0 cm elongation of the spring.

3. What is Spring Constant? F=kx Ans. 490N/m

4. What is the force required to stretch 8.5 cm? F=kx Ans. 41.65N SHM Ex.When a mass is suspended from a spring and in equilibrium, the spring extends by 10 cm. The

mass receives a slight push up and oscillates. What is the period of the oscillations?

mg=kx & T=2pi *sqrt(m/k) Ans. .63 secs Ex. A mass (m = 50 kg) is attached to a spring (k = 5 N/m) and is at an initial position x0 = + 5 m and has an initial velocity v0 = + 5.50 m/s.

2. Find angular frequency? w=sqrt(k/m) Ans. .316rad/s

3. Find the amplitude? X(t) = A*cos(wt +Y) Ans. 18.1m Energy of SHM Pendulum & UCM EX. I have a pendulum length 90m.

1. What is period? T= 2pi *sqrt(L/g) Ans.19.0s EX. My pendulum defies all the laws of physics and oscillates 20 times in 70 seconds.

2. What is the frequency? F= #revs/total time Ans. .286 Hz

3. What is Period? T = 1/F Ans. 3.5 secs

4. What is the length? T= 2pi*sqrt(L/g) Ans. 3m if g=10 Conclusion Since Mechanics is the study of the relationship between motion, force and energy, oscillations fit in this frame of study simply because it involves all three concepts of mechanics. Oscillations explain the fluctuating pattern or rhythm to some forms of motion and is particularly useful in studying waves. With the application of Oscillatory motion it is possible to delve into the world of Quantum mechanics and possibly disprove the existing laws of the universe. Topics: Pendulums; UCM & SHM Vocabulary: Pendulums; UCM & SHM Simple Harmonic Motion (Pendulum) Constant Time Period, returns to beginning position and restarts motion Simple Harmonic Motion (Spring) Energy of Simple Harmonic Motion Kinetic and Potential Energy are inversely proportional to each other Uniform Circular Motion Circular path at a constant speed SHM Equations Period of Oscillation:

T = 2 (M/k) Velocity:

v = 1/(2 ) UCM Equations Velocity:

v= (2 r)/t Acceleration:

(v )/r Net Force:

F=ma The Simple Pendulum

The Physical Pendulum

The Torsional Pendulum oscillatory motion

simple harmonic motion

periodic motion

damped motion

forced motion

simple pendulum

physical pendulum

torsion pendulum displacement function

velocity function

acceleration function

amplitude

time period

frequency

angular frequency

phase constant

phase

energy functions amplitude

time period

frequency

angular frequency

phase constant

phase

energy functions

force function

momentum function frequency

phase constant

energy functions

force function

momentum function

underdamped system

critically damped system

overdamped force function

momentum function

underdamped system

critically damped system

overdamped

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