A 3.60-kg object is attached to a spring and placed on frictionless, horizontal

Question

A 3.60-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 30.0 N is requierd 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 subseuently undergoes simple harmonic oscillations. Find the force constant of the spring Find the frequency of the oscillations. Find the maximum speed of the object. Where does this maximum speed occur? x = plusminus Find the maximum acceleration of the object.

Explanation / Answer

m = mass of object = 3.60 kg

F = force = 30 N

x = distance = 0.200 m

a) k= spring constant = ?

F = kx [ consider magnitude only]

k = F/ x

= 30 / 0.200

k = 150 N/m

b) f = frequency = ?

k = m*w2

w ( angular frequency) = ( k/m)1/2

= ( 150 / 3.60)1/2

w = 6.45 rad/s

w = 2*pi*f

f = 6.45/ 2*3.14

f = 1.02 hz

c) Vmax ( maximum speed) = w*A

A = amplitude ( or maximum displacement) = 0.200m

Vmax = 6.45*0.200 = 1.29 m/s

d) max speed occur at x = +- 0 m ( ie at mean position)

e) a_max ( maximum acceleration) = w2*A

= ( 6.45)2*0.200 = 8.32 m/s2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.