14.9 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

(iii) The maximum speed of the mass

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Vishal Baghel | Contributor-Level 10

5 months ago

Spring constant, k = 1200 N/m

Mass, m = 3 kg

Displacement, d = 2 cm = 0.02 m

(a) Frequency of oscillation, v is given by

v = $\frac{1}{T}$ = $\frac{1}{2 π} \sqrt{\frac{k}{m}}$ = $\frac{1}{2 π} \sqrt{\frac{1200}{3}}$ = 3.183 m/s

(b) Maximum acceleration (a) is given by the relation: a = $ω^{2} A$

where, $ω =$ angular frequency = $\sqrt{\frac{k}{m}}$ and A = maximum displacement

a = $\frac{k A}{m}$ = $\frac{1200 \times 0.02}{3}$ = 8 m/ $s^{2}$

(c) Maximum velocity, $v_{m a x} = A ω = A \sqrt{\frac{k}{m}}$ = $0.02 \sqrt{\frac{1200}{3}}$ = 0.4 m/s

Hence the maximum velocity of the mass is 0.4 m/s

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