Answer:
a. The angular frequency is doubled.
e. The period is reduced to one-half of what it was.
Explanation:
Angular frequency is given as;
ω = 2πf
[tex]\frac{\omega _1}{f_1} = \frac{\omega _2}{f_2}[/tex]
when the frequency is doubled
[tex]\frac{\omega _1}{f_1} = \frac{\omega _2}{(2f_1)} \\\\\omega _1 = \frac{\omega _2}{2}\\\\\omega _2 = 2\omega _1[/tex]
Thus, the angular frequency will be doubled.
Amplitude in simple harmonic motion is the maximum displacement.
Frequency is related to period in simple harmonic motion as given in the equation below;
[tex]f = \frac{1}{T} \\\\f_1T_1= f_2T_2\\\\T_2 = \frac{f_1T_1}{f_2}[/tex]
when the frequency is doubled;
[tex]T_2 = \frac{f_1T_1}{2f_1} \\\\T_2 = \frac{T_1}{2}[/tex]
Thus, the period will be reduced to one-half of what it was.
