Answer
The factors are:
a) 1
b) 1
c) 1
d) 2
e) 2
f) 4
Work Step by Step
(a) We know that $\omega=\frac{2\pi}{T}$. This equation shows that the angular frequency does not depend on the amplitude; hence the angular frequency does not change.
(b) We know that $f=\frac{1}{T}$. Since the frequency depends on time period, not amplitude, it doesn't change.
(c) We know that the time period remains the same.
(d) The maximum speed is given as
$v_{max}=A\omega$
$\implies v_{max}=(2A)\omega$
$\implies v_{max}=2(A\omega)$
Thus, the maximum speed is doubled.
(e) We know that
$a_{max}=A\omega^2$
$\implies a_{max}=2A\omega^2$
$\implies a_{max}=2(A\omega^2)$
Thus, the maximum acceleration is doubled.
(f) The total mechanical energy is given as:
$E=\frac{1}{2}m\omega^2A^2$
$\implies E=\frac{1}{2}m\omega^2(2A)^2$
$\implies E=4(\frac{1}{2}m\omega^2A^2)$
Thus, the total mechanical energy increases four times.
