Answer
(a) $0.13m$
(b) $84N/m$
(c) $0.83Hz$
Work Step by Step
(a) We can find the amplitude as follows:
$A=\frac{mv_{max}^2}{F_{max}}$
We plug in the known values to obtain:
$A=\frac{(3.1Kg)(0.68m/s^2)}{11N}$
$A=0.13m$
(b) The force constant can be determined as follows:
$\omega=\frac{F_{max}}{mv_{max}}$
$\implies \omega=\frac{11N}{(3.1Kg)(0.68m/s)}=5.2rad/s$
Now $K=m\omega^2$
We plug in the known values to obtain:
$K=(3.1Kg)(5.2rad/s)^2$
$K=84N/m$
(c) The required frequency can be determined as:
$m\omega=\frac{F_{max}}{V_{max}}$
$m\omega=\frac{11}{0.68}=16.176$
$\implies \omega(3.1)=16.176$
$\implies \omega=5.218$
Now $f=\frac{5.218}{2\pi}$
$f=0.83Hz$
