A 1.55kg mass is attached to a spring and placed on a horizontal, smooth surface

Question

A 1.55kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 14.8N is required to hold the mass at rest when it is pulled 0.247m from its equilibrium position (the origin of the x axis). The mass is now released from rest with an initial displacement of x = 0.247m, and it subsequently undergoes simple harmonic oscillations. Calculate the force constant of the spring. (For reference, read section 12.2 of the 5th edition of Serway and Jewett's "Principles of Physics") What is the spring constant? What is the maximum speed? What is the maximum magnitude of the acceleration? What is the total energy of the mass and spring? What is the speed of the mass when it's displacement is one fifth of the maximum value? What is the magnitude of the acceleration of the mass when it's displacement is one fifth of the maximum value?

Explanation / Answer

here,

horizontal force , F = 14.8 N

amplitude , A = 0.247 m

mass , m = 1.55 kg

a)

let the spring constant be K

F = k * A

14.8 = K * 0.247

K = 59.9 N/m

b)

the frequency of oscillation , f = 1/2pi * sqrt(k/m)

f = 1/2pi * sqrt( 59.9/1.55)

f = 1 Hz

c)

the maximum speed , v = A * 2 * pi * f

v = 0.247 * 2 * pi * 1

v = 1.54 m/s

d)

the magnitude of maximum accelration , amax = A * (2 * pi * f)^2

amax = 0.247 * ( 2 * pi * 1)^2

amax = 9.74 m/s^2

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