A 1.00-kg glider attached to a spring with a force constant 9.0 N/m oscillates o

Question

A 1.00-kg glider attached to a spring with a force constant 9.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -3.30 cm (that is, the spring is compressed by 3.30 cm). Find the period of the glider's motion. Find the maximum values of its speed and acceleration, speed. Find the position, velocity, and acceleration as functions of time. (Where position is in m, velocity is in m/s, acceleration is in m/s^2, and t is in s. Use the following as necessary: t.)

Explanation / Answer

Here,

a)

for the period of the glider

T = 2pi * sqrt(m/k)

T = 2pi * sqrt(1/9)

T = 2.094 s

the perdiod of glider is 2.094 s

b)

let the maximum speed of the glider is v

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

1 * v^2 = 9 * 0.033^2

v = 0.099 m/s

the maximum value of v is 0.099 m/s

for the maximum value of acceleration

maximum value of acceleration = A * (2pi/T)^2

maximum value of acceleration = 0.033 * (2pi/2.094)^2

maximum value of acceleration = 0.297 m/s^2

the maximum value of acceleration is 0.297 m/s^2

c)

for the position

as x = A * cos(2pi * t/T)

x = 0.033 * cos(2pi * t/2.094)

for the velocity

v = - Vmax * sin(2pi * t/T)

v = -0.099 * sin(2pi * t/2.094)

for the acceleration

a = - amax * cos(2pi * t/T)

a = - 0.297 * cos(2pi * t/2.094)

the accelearion is - 0.297 * cos(2pi * t/2.094)

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