Question

26. An oscillator of mass 10 gram is oscillating with
natural frequency of 100 Hz. Under slight damped
· conditions, a periodic force F = 100 cos20nt is
applied on it. Amplitude of oscillation is
approximately :-
(1) 0.025 cm
(2) 2.5 cm
(3) 0.25 cm
(4) 25 cm​

Answer 1

Answer:

The correct answer is 0.25cm

Answer 2

Answer:

The approximate value of Amplitude of oscillation is 0.025 cm

Explanation:

Given as :

Mass of oscillator = 10 gram = 0.01 kg

Natural frequency = f = 100 Hz

periodic force = F = 100 cos 20nt

Let The Amplitude of oscillation = A cm

According to question

For oscillation

Force = mass × (angular frequency)² × Amplitude

Or, 100 = 0.01 × ω² × A

Or, 100 = 0.01 × ( 2 π f ) × A

or, 100 = 0.01 × ( 2 × 3.14 × 100 )² × A

Or, 100 = 0.01 × ( 628 )² × A

Or, 100 = 3943.84 × A

∴    A = $\dfrac{100}{3943.84}$

i.e A = 0.025 cm

Hence, The approximate value of Amplitude of oscillation is 0.025 cm Answer