# Class 11 Physics Oscillations: NCERT Solutions for Question 9

This page focuses on the detailed Oscillations question answers for Class 11 Physics Oscillations, addressing the 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.'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 9

## 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.

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, VMAX = ω A

= 0.02 X √1200/3

Therefore, VMAX = 0.4 m / s

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