A4.00-kg object is attached to a spring and placed on frictionless, horizontal surface. a horizontal force of 27.0 n is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). the object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations.
(a) find the force constant of the spring.
n/m
(b) find the frequency of the oscillations.
hz
(c) find the maximum speed of the object.
m/s
(d) where does this maximum speed occur?
x = ± m
(e) find the maximum acceleration of the object.
m/s2
(f) where does the maximum acceleration occur?
x = ± m
(g) find the total energy of the oscillating system.
j
(h) find the speed of the object when its position is equal to one-third of the maximum value.
m/s
(i) find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value.
m/s^2

a)

Nm⁻¹

b)

Hz

c)

ms⁻¹

d)

m

e)

ms⁻²

f)

m

Explanation:

a)

= force required to hold the object at rest connected with stretched spring = 27 N

= stretch in the spring from equilibrium position = 0.2 m

= force constant of the spring

force required to hold the object at rest is same as the spring force , hence

inserting the values

Nm⁻¹

b)

frequency of the oscillations is given as

inserting the values

Hz

c)

= Amplitude of oscillations = 0.2 m

= angular frequency

Angular frequency is given as

rads⁻¹

Maximum speed of oscillation is given as

ms⁻¹

d)

maximum speed of the object occurs at the equilibrium position, hence

m

e)

Maximum acceleration of oscillation is given as

ms⁻²

f)

maximum acceleration occurs when the object is at extreme positions, hence

m

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hope this : d