11P13 Oscillations

What is the relation between circular motion and Oscillatory Motion,

Rotating Vectors,Phasors

How is Circular motion linked with Simple Harmonic Motion SHM?
What is the phase difference between Displacement, Velocity and Acceleration?
How does the amplitude of each above quantity change as the angular velocity w change?
What are Phasors (Rotating Vectors)? (Alternating Current)

Adjust the length of the pendulum to study how it changes the time period of oscillation

How to find the gravity in your neighbourhood using a simple pendulum? (The gravity g=9.81 m/s2) is not a constant in all the locations of earth. It varies from equator to poles along different latitudes due to the radius measured from the center of the earth and also due to the centrifugal force.)

What is the formula for Time Period of a Spring-Mass oscillating system?

Change the mass or spring constant K to see the effect it has on the Time period.

Does your observation agree with the formula prediction?

Observe the Velocity, Acceleration vectors' directions and explain them w.r.t to displacement from the mass equilibrium line shown. Hence explain how it is SHM.

https://www.geogebra.org/calculator/gw9mnafb

Help for NCERT example and exercise numerical

To find the time period of the curve cos(wt) + cos(3wt) + cos(5wt)

Find the LCM of the time period of each part 

which is 2pi / w, 2pi/3w, 2pi/5w which is 2pi/w

Also observe the same in the resultant red graph

(Read w as omega, pi is 3.14)

What is Resonance?

What is Resonance in Oscillating systems such as Spring and Mass system?

Find the Natural Frequency of each of the spring mass system and show that it will oscillate with maximum displacement during Resonance?

(Sol: Use the frequency formula for spring mass system freq=(1/2 pi) sqrt(k/m) 

Natural frequency of each system is 0.8 Hz, 1.1 Hz, 1.6 Hz respectively)

Lissajous Figures  Academo.org

Oscillation in two dimensions of X and Y axis gives rise to a pattern named Lissajous Figures.