Department of Natural Sciences

Clayton College & State University

 

December 1, 2004

 

Physics 2211 – Quiz 11

 

 

Name  _____SOLUTION________________________________

 

A 1.50-kg mass on a spring has displacement as a function of time given by the equation      

                      

                                     x(t) = (7.40 cm) cos[(4.16 s-1)t – 2.42].

 

Find

  1. The time for one complete oscillation.

 

A = 7.40 cm = 0.0740 m

w = 4.16 rad/s

f = -2.42 rad

 

T = 2p /w =  2p /(4.16 rad/s) = 1.51 s

 

  1. The force constant of a spring.

 

w2 = k/m

k = w2m

 

k = (4.16 rad/s)2 (1.50 kg) = 26.0 N/m

 

  1. The maximum speed of the mass.

 

Vmax = w A

 

Vmax = (4.16 rad/s)(0.0740 m) = 0.308 m/s

 

  1. The maximum force on the mass.

 

Fmax = k A

 

Fmax = (26.0 N/m) (0.0740 m) = 1.92 N

 

 

  1. The speed of the mass at t = 1.00 s.

 

V(t) = - (0.740 m)(4.16 rad/s) sin[(4.16 s-1(1.00 s) – 2.42] = - 0.303 m/s

 

V = 0.303 m/s