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Class 11
Physics
Oscillations
a spring having with a spring constant 1200 n m 1...

Question:
A spring having with a spring constant 1200 N m-1 is mounted on a horizontal table as shown in Fig. 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.

Answer:

Given, Spring constant, k = 1200 N/m

Mass, m = 6 kg

Displacement, A = 4.0 cm = 0.04 cm

( i ) Oscillation frequency v = 1/T = 1/2π √k/m

Where,T = time period.

Therefore v =1/2×3.14 √1200/3 = 3.18m/s

Hence, the frequency of oscillations is 3.18 cycles per second.

( ii ) Maximum acceleration (a) = ω² A

Where, ω = Angular frequency = √k/m

A = maximum displacement

Therefore, a = A( k/m )

a = 0.02 x (1200/3 ) = 8 m /s^-2

( iii ) Maximum velocity, V_MAX= ω A

= 0.02 X √1200/3

Therefore, V_MAX= 0.4 m / s

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

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