A frictionless, horizontal, simple, harmonic oscillator of mass 0.28 kg and poss

Question

A frictionless, horizontal, simple, harmonic oscillator of mass 0.28 kg and possesses 18 m of mechanical energy. (a) The oscillator is set into motion with a 2.5-cm amplitude. What is the period? (b) What is the stiffness of the spring? (c) How far from equilibrium will the oscillator be when traveling at 0.20 m/s? (d) What is the maximum acceleration of the oscillator? (e) A linearly damped oscillator with the same mass and initial mechanical energy generates 15 m of thermal energy in 4.0 s. Find the damping constant b.

Explanation / Answer

here,

mass , m = 0.28 kg

mechanical energy , ME = 18 mJ = 0.018 J

a)

A = 2.5 cm = 0.025 m

let the spring constant be k

0.5 * k * A^2 = ME

0.5 * k * 0.025^2 = 0.018

k = 57.6 N/m

the period , T = 2 * pi * sqrt(m/k)

T = 2 * pi * sqrt(0.28 /57.6)

T = 0.44 s

b)

the stiffness constant is 57.6 N/m

c)

when v = 0.2 m/s

let the distance from the equilibrium point be x

0.5 * m * v^2 + 0.5 * k * x^2 = ME

0.5 * 0.28 * 0.2^2 + 0.5 * 57.6 * x^2 = 0.018

x = 0.02 m

d)

the maximum accelration , a = w^2 * A

a = (2 * pi /T)^2 * A

a = (2 * pi /0.44)^2 * 0.025 m/s^2

a = 5.1 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---