^Pendulum in accelerated frame

^Pendulum in accelerated frame

Suppose a simple pendulum is hanging in a truck speeding up horizontally tight side with acceleration ‘a’ w.r.t. stationary ground, then

From the ground frame

1. Tsinθ gives the pendulum x acceleration (a)

i.e. Tsinθ = ma

2. Tcosθ balances the weight of the pendulum

i.e. Tcosθ = mg

From the truck frame

1. the pendulum is in eqbm. Under the influence of three forces pseudo force, weight & tension in string,  i.e.,
2. Tsinθ balances the x force on pendulum i.e. Tsinθ = ma
3. Tcosθ balances the weight of the pendulum i.e. Tcosθ = mg                                                                             Note from both the final rearrangement of equations gives same relations. Also from the drawings or equations we can write