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 1

(a) spring constant ( K ) = 1200 N/m
mass ( m ) = 3 Kg
Amplitude ( A) = 20 cm = 20 × 10^-2 m
Now, use formula for frequency of oscillation .
f = 1/2π √{ K/m}
= 1/2 ×3.14 √{ 1200/3}
= 20/6.28
= 3.2 /s

(b) maximum acceleration = w²A
= (2π × f )² A
= (2π × 1/2π√(K/m)}²A
= K/m.A
= 1200/3 × 2 × 10^-2
= 8 m/s²

(c) maximum speed = wA
= √(K/m) × A
= √(1200/3) × 2 × 10^-2
= 20 × 2 × 10^-2
= 4 m/s