The given wave equation is:
Y=10sin‌(‌+α)At
t=0, the displacement
Y is given as
5‌cm. So, let's find the phase
α using this information:
‌5=10sin‌(α)‌‌=‌=sin‌(α) Since
sin‌(30∘)=‌, we can say that
α=30∘ or
α=‌ radians, considering that sine is positive in the first and second quadrants, and seeing that
α represents a phase shift, it usually takes the smallest positive angle that satisfies the equation.
Now, let's calculate the total phase at
t=7.5 s :
Total phase
=‌+αPlug in the values:
Total phase
=‌+‌Total phase
=‌+‌=‌+‌ To add these fractions, we first find a common denominator :
Total phase
=‌+‌=‌Now we simplify the fraction:
Total phase
=‌Therefore, the total phase at
t=7.5 s is
‌ radians, which corresponds to Option D.