After t minutes, the height h meters above the ground of the seat is given by #h=74+acosbt#. How do you show that the period of h is 25 minutes?

Question

2463 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-21T14:19:58

In order for the period to be #=25mn#, the value of #b=0.25#

The function is

#h(t)=74+acosbt#..........................#(1)#

For a periodic function of period #T#

#h(t)=h(t+T)#

#h(t+T)=74+acosb(t+T)#

#=74+acos(bt+bT)#

#=74+acosbtcosbT-asinbtsinbT#.............#(2)#

Comparing this equation to equation #(1)#

#{(cosbT=1),(sinbT=0):}#

#<=>#, #bT=2pi#

#<=>#, #T=2/bpi#

In order for #T=25mn#

#2/bpi=25#

#=>#, #b=(2pi)/25=0.25#