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A spring having with a spring constant 1...

A spring having with a spring constant `1200 N m^(-1)` is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.

Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

Text Solution

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Here `k=120Nm^(-1)mm=3.0kg,A=2.0cm=0.02m`
a. Frequency `f=1/T=1/(2A)sqrt(k/m)=1/(2xx3.14)sqrt(1200/3)=3.2s^(-1)`
b. Acceleration `a=omega^(2)y=k/m y`
Acceletaration will be maximum when y is maximum i.e. y=A
`:.` Max acceleration `a_("max")=(kA)/m=(1200xx0.02)/3=8ms^(-2)`
c. Max. speed of the mass will be when it is passing through the mean position whcih is given by
`V_("max")=Aomega=Asqrt(k/m)=0.02xxsqrt(1200/3)=0.4ms^(-1)`
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