A spring having a spring constant `1200Mn^(-1)` is mounted on a horizontal table. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 0.02 m and released. Determine (i) frequency of oscillations (ii) maximum acceleration of the mass and (iii) the maximum speed of the mass.

Explanation

Given, `k=1200Nm^(-1), m=3kg, y=0.02 m`

(i) Frequency of oscillation, `f=(1)/(2pi)sqrt((k)/(m))`
i.e. `f=((1)/(2xx3.142))sqrt((1200)/(3))=(10)/(3.142)=((10)/(pi))Hz`
(ii) maximum acceleration of the mass,
`a_("max")=-omega^(2)y` where `omega=(2pi)/(T)=2pif`
`"i.e. "omega=2pixx(10)/(pi)`
hence `a_("max")=-20xx20xx0.02`
`a_("max")=8ms^(-2)`
(iii) maximum speed of the mass,
`v_("max")=omegaA=2xx0.02 =0.4ms^(-1)`.