Question

Motion of an oscillating mass [0.75 kg] attached to the spring is described by the equation below:
(??) = 7.4 (????) ?????? [(4.16 ?????? ?? ) ?? ? 2.42]
Find:
a. Amplitude
b. Frequency
c. Time Period
d. Spring constant
e. Velocity at the mean position
f. Potential energy
g. at the extreme position.

Answer 1

given

mass m = 0.75 kg

attached to a spring of spring constant k

equatiion

x(t) = 7.4 cm Cos(4.16 rad/s t - 2.42)

comparing with x(t) = Acos(wt - phi)

a. amplitude, A = 7.4 cm

b. freuency = f

f = w/2pi

f = 4.16/2*pi = 0.66208456326 Hz

c. time period T = 1/f = 1.51038108345663 s

d. spring constat = k

now, T = 2*pi*sqroot(m/k)

hence

k = 12.9792 N/m

e. Velocity at mean position = A*w = 30.784 cm/s

f. PE = 0.5*k*x^2 = 6.4896*(7.4^2) cos^2(4.16t - 2.42)

PE = 0.035537049*cos^2(4.16t - 2.42) J

g. PE at extreme position

PE = 0.5*k*A^2 = 0.0355370496 J