Question

The position of a 46 g oscillating mass is given byx(t)=(2.0cm)cos13t, where t is in seconds.

Determine the amplitude.
Determine the period.
Determine the spring constant.
Determine the maximum speed.
Determine the total energy
Determine the velocity at t = 0.43s

Answer 1

Here ,

x = 2 cm cos(13t)

comparing it to

x = A * cos(w * t)

amplitude , A = 2 cm

w = 13 rad/s

time period = 2pi/w = 2pi/13

time period = 0.48 s

---------------------------------

as w = sqrt(k/m)

13 = sqrt(k/.046)

k = 7.77 N/m

the spring constant is 7.77 N/m

---------------------------

maximum speed = A * w

maximum speed = 0.02 * 13 = 0.26 m/s

------------------------

total energy = maximum kinetic energy

total energy = 0.50 * 0.046 * 0.26^2

total energy = 1.55 *10^-3 J

-------------------

v = dx/dt

v = - 0.02 * 13 * sin(13 * t)

v = - 0.02 * 13 * sin(13 * 0.43)

v = -0.025 m/s

the velocity at t = 0.43 s is - 0.025 m/s