Question

The position of a 47 g oscillating mass is given by x(t)=(1.7cm)cos13t, where t is in seconds.

A: Determine the amplitude.

B. Determine the period

C. Determine the Spring constant.

D. Determine the maximum speed.

E. Determine the total energy.

F. Determine the velocity at t = 0.45s

I am able to check the answers, but I'm not sure what the process is to get the answer. Every method I try isn't getting me to the right answers.

Answers are: A: A = 1.7cm B:T = 0.48s C: k = 7.9N/m D: v_max = 0.22m/s E: W _total = 1.1 * 10^-3F: v = 9.3 * 10^-2 m/s

Answer 1

mass m = 47 g= 0.047 kg

x(t)=(1.7cm)cos13t, where t is in seconds.

Compare this x(t) = A cos wt you get ,

A = 1.7 cm

w = 13 rad/s

A: the amplitude. A = 1.7 cm

B. the period T = 2(pi) / w

= 2(3.1415) / 13

= 0.4833 s

C. the Spring constant k = mw ²

= 0.047 x13 ²

= 7.943 N/m

D. the maximum speed V = Aw

= (1.7 cm) (13 rad/s)

= 22.1 cm/s

= 0.221 m/s

E. the total energy E = (1/2) kA ²

= 0.5 x7.943 x (1.7 x10 ^-2 ) ²

= 1.147 x10 ^-3 J

F. the velocity at t = 0.45s isv(t) = ?

We know v(t) = dx(t) / dt

= (1.7cm)(13) sin(13t)

= (22.1 cm/s) sin 13t

= (0.221 m/s) sin 13 t

v(0.45) = (0.221) sin (13x0.45)

= (0.221) sin 5.85

= 0.221(-0.4197)

= -0.09276 m/s