Question

An oscillator consists of a block of mass 0.900 kg connected to a spring. When set into oscillation with amplitude 27.0 cm, it is observed to repeat its motion every 0.400 s.

(a) Find the period.

s

(b) Find the frequency.

hz

(c) Find the angular frequency.

rad/s

(d) Find the spring constant.

N/m

(e) Find the maximum speed.

m/s

(f) Find the maximum force exerted on the block.

N

please show work and answer

Answer #1

here,

mass of block, m = 0.9 kg

amplitude, x = 27 cm = 0.27 m

time, t = 0.4s

part a:

period, p = time of one complete oscillation

period, p = t = 0.4 s

Part b:

freqency, f = 1/p

freqency, f = 1/0.4

Frequency,f = 2.5 Hz

Part c:

angular frequency, w = 2*pi*f

angular frequency, w = 2*pi*2.5

angular frequency, w = 15.708 rad/s

part d:

spring constant, k = m*w^2

spring constant, k = 0.9*15.708^2

spring constant, k = 222.067 N/m

part e:

Vmax = x * w

Vmax = 0.27 * 15.708

Vmax = 4.241 m/s

part f:

Max Force, F = k *x

Max Force, F = 222.067 * 0.27

Max Force, F = 60 N

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