Problem # 3 (24 pts ) A 2.00 kg mass on a frictionless surface is attached to a

Question

Problem # 3 (24 pts ) A 2.00 kg mass on a frictionless surface is attached to a spring o nknown spring constant &. The displacement of the center of the mass is given by -4union usintsoa Xlt): (.loon.) si n [Suo0H a) Find the time to complete one cycle b) Find the maximum speed of the mas 2 2 nf c) Find the maximum force on the mass d) Find the force constant k of the spring. (25)(2): so e) Find the position of the mass at time t 2.00s. (Both magnitude and direction) Find the acceleration of the mass at time t 2.00 s. (Both magnitude and direction) 2.n alt):R'sin (s.ub(?))= 2

Explanation / Answer

given, mass m = 2 kg
frictionless surface
spring constant = k

x(t) = 0.1m sin(5t)

a. time period T = 2*pi/w = 2*pi/5 = 1.2566 s
b. Maximum speed, Vmax = Aw = 0.1*5 = 0.5 m/s
c. maximum force = m*amax
   amax = A*w^2 = 0.1*25 = 2.5 m/s/s
   Fmax = 2.5*2 = 5 N
d. spring constant = k
   w = sqroot(k/m)
   w^2*m = k = 25*2
   k = 50 N/m
e. at t = 2s
   x(t) = 0.1*sin(10) = 0.1*sin(10*180/pi deg) = -0.0544 m
f. at t= 2s
   a = -w^2x = 1.36 m/s/s

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