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.

Question

Philoid · Accepted Answer

Here, Spring Constant,K = 1200N/m

Mass,m = 3 kg

Distance travelled by mass,a = 2 cm = 0.2 m

(i) Frequency, v = 1/T = 1/2π√k/m

= 1/2×3.14√1200/3

= 3.2 /s

(ii) Acceleration, A = (k/m)y

When y = a i.e maximum, acceleration will be maximum

Hence,A_max = (ka)/m

= (1200×0.02)/3

= 8 m/s²

(iii) When the mass will be passing through mean position, it will have maximum speed.

V_max = a√(k/m) = 0.02×√(1200/3)

= 0.4 m/s.