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