SIMPLE HARMONIC MOTION

                                                 Tips & Tricks

1. The time period of a simple pendulum is 

                                                                T = 2 .

                                                         =>  T  or  

                                                          

                                            

                                                        =>   

                                                         

Using these relations. We may conclude

(i)     The graph between T² and l is a straight line. 

(ii) The graph between T and l is a parabola.

(iii)The graphs l-T and l-T² intersect at T=1s

(iv) The graph between T² and 1/g is a straight line.

(v)The graph between T² and g is a rectangular hyperbola.

(vi)   Finally, the graph between T and is also a straight line.

2. In the case of water oscillating in a U-tube

                                                    T = 2pi  .
                   
    3.  Where, h is the height of liquid column in each limb. When a ball of mass m is made to oscillate in the neck of an air chamber having volume V, neck area A, and d is the density of the liquid then

                                           T = .

4. When a pendulum is kept in a car which is sliding down, then 

                                      

                                                T =2 . Where, theta is the angle of inclination