A 110 kg mass on a spring has displacement as a function of

A 1.10 kg mass on a spring has displacement as a function of time given by the equation x(t)=(7.40cm)cos[(4.16rad/s)t2.42rad].

A.) Find the time for one complete vibration.

B.) Find the force constant of the spring.

C.) Find the maximum speed of the mass.

D.) Find the maximum magnitude of force on the mass.

E.) Find the position of the mass at t=1.00s;

F.) Find the speed of the mass at t=1.00s;

G.) Find the magnitude of acceleration of the mass at t=1.00s;

H.) Find the magnitude of force on the mass at t=1.00s;

The motion of the spring is of the form

X(t) = ACos(t+)

A= 7.4 cm , = 4.16 rads/s , = -2.42 rads

Mass m = 1.10 kg

Find the time for one complete vibration.

Period of vibration T = 2/ = 1.51 s

Find the force constant of the spring.

= (k/m) = 4.16

spring constant k = (4.16)² x1.1 = 19.04 N/m

Find the maximum speed of the mass.

Velocity v = dx/dt = ASin(t+)

Maximum speed = A = 0.074*4.16 =0.3078 m/s

Find the maximum magnitude of force on the mass.

Maximum Force F = A² = 7.4x(4.16)² = 128.06 N

Find the position of the mass at t=1.00s;

X(t=1)=(7.40cm)cos[4.162.42]. = -1.25 cm

Find the speed of the mass at t=1.00s;

V(t=1) = ASin(t+) = 7.4*4.16Sin(4.16*1-2.42)

=30.34 cm/s = 0.3034 m/s

Find the magnitude of acceleration of the mass at t=1.00s;

Acceleration a = dv/dt = -A² Cos(t+)

A(t=1) = 7.4*(4.16)² Cos(4.16-2.42)

= 21.57 cm/s² = 0.2157m/s²

Find the magnitude of force on the mass at t=1.00s;

F = ma = 1.1*0.2157 = 0.2372 N