Question

An object is undergoing simple harmonic motion along the x-axis. its position is described as a function of time by x(t)= 5.3cos(4.2t-1.9), where x is in meters, the time t, is in seconds, and the argument of the cosine is in radians.

c) determine the position of the object, in meters, at the time t=2.6s?

d) what the objects velocity, in meters per second, at the time t=2.6s?

e) calculate the objects acceleration, in meters per second squared, at time t=2.6s?

f) what is the objects maximum acceleration, in meters per second squared?

g) what is the magnitude of the objects maximum velocity, in meters per second?

Answer 1

here,

x(t) = 5.3 * cos(4.2 t - 1.9)

c)

at t = 2.6 s

the position , x(2.6) = 5.3 * cos(4.2* 2.6 - 1.9) m

x(2.6) = - 4.88 m

d)

the object velocity , v(t) = dx /dt

v(t) = 5.3 * 4.2 * (- sin(4.2 t - 1.9))

v(t) = 22.26 m/s * (- sin(4.2 t - 1.9))

at t = 2.6 s

v(2.6) = 22.26 * (- sin(4.2 * 2.6 - 1.9)) m/s

v(2.6) = - 8.67 m/s

e)

a(t) = dv(t) /dt

a(t) = 22.26 * 4.2 * (- cos(4.2 * t - 1.9))

at t = 2.6 s

a(2.6) = 94.33 m/s^2 * (- cos(4.2 * 2.6 - 1.9))

a(2.6) = 86.9 m/s^2

f)

the maximum acceleration ,am = 94.33 m/s^2

g)

the magnitude of object maximum velocity is 22.6 m/s