Saved Bookmarks
| 1. |
A body oscillates with SHM according to the equation `x(t)=5cos(2pit+pi//4)` where t is in second and x in metres. Calculate (a) displacement at t=0 (b) time period (c) initial velocity |
|
Answer» `x(t)=5cos(2pit+pi//4)` …(i) (a) At `t=0,` displacement, `x(0)=5cos(2pixx0+pi//4)` or `x(0)=5cospi//4=(5)/(sqrt(2))m` (b) Comparing (i) with the standard equation of SHM. `x(t)=Acos(omegat+phi_(0)),` we have `omega=2pi or (2pi)/(T)=2pi or T=1s` (c) Velocity, `upsilon=(dx)/(dt)` `=[-5sin(2pit+pi//4)]xx2pi` At `t=0,` initial velocity, `upsilon_(0)=[-5sin(2pixx0+pi//4)]xx2pi` `=(-10pi)/(sqrt(2))=-5sqrt(2)pims^(-1)` |
|