Question

An oscillator consists of a block of mass 0.628 kg connected to a spring. When set into oscillation with amplitude 27 cm, the oscillator repeats its motion every 0.372 s. Find the

(a) period,
(b) frequency,
(c) angular frequency,
(d) spring constant,
(e) maximum speed, and
(f) magnitude of the maximum force on the block from the spring.

Answer 1

T=0.372 s, f=2.7 Hz, w=16.9 rad/s, k=179.2 N/m, v= 8.78 m/s, F= 48.4 N

Step-by-step explanation:

a.)

Period: It is already given in the question "oscillator repeats its motion every 0.372 s".

So T=0.372 s

b)

frequency= f = 1/ T

f = 1/ 0.372

f=2.7 Hz

c).

Angular frequency= w= 2πf

w= 2*π*2.7

w=16.9 rad/s

d)

Spring Constant:

As w=
`√(k/m)`

⇒w²= k/m

⇒k= m*w²

⇒k= 0.628 * 16.9² N/m

⇒k=179.2 N/m

e)

The mass will have maximum speed when it passes through the mean position.

At mean position

Maximum elastic potential energy = Maximum kinetic energy

1/2 k A² = 1/2 m v² ( A is amplitude of oscillation)

⇒ v=
`√(k A^2/m)`

⇒ v=
`√(179.2 * 0.27/ 0.628)`\

⇒ v= 8.78 m/s

f)

Maximum force will be exerted on the block when it is at maximum distance.

F= k* A ( A is amplitude of oscillation)

F= 179.2 * 0.27 N

F= 48.4 N