1. (20 pts)The figure gives the position (in cm) as a function of time (in ms) o

Question

1. (20 pts)The figure gives the position (in cm) as a function of time (in ms) of a block with mass m attached to a spring with spring constant k.

(a) (2pts) What is the period of oscillation? (b) (3pts) Calculate the maximum speed of the block. (c) (3pts) The spring exerts a maximum force of 110 N on the block. What is the mass of the block? (d) (3pts) What is the spring constant of the spring?

(e) (2pts) What is the phase constant for SHM if the position function of x(t) has the form x(t) = xm cos(wt +(theta))?

(f) (7 pts) Label the points in the figure that correspond to the minimum and maximum values of kinetic and potential energy.

1·(20 pts)The figure gives the position(in cm) as a function of time(in ms) of a block with mass m attached to a spring with spring constant k æ (cm) 4 3 2 t (ms 3.4 1 2.6 8.6 6 4 (a) (2pts) What is the period of oscillation? (b) (3pts) Calculate the maximum speed of the block (c) (3pts) The spring exerts a maximum force of 110 N on the block. What is the mass of the block? (d) (3pts) What is the spring constant of the spring? (e) (2pts) What is the phase constant for SHM if the position function of x(t) has the form x(t)-X,n cos(ot + )? 7 pts) Label the points in the figure that correspond to the minimum and maximum values of kinetic and potential energy

Explanation / Answer

1) a)
goes from max in min in 6 seconds

so period = 2*6 = 12 ms

b) vmax = A w = 2 pi A/T = 2*pi*0.04/0.012=20.94 m/s

c) Fmax = m amax

amax = w^2 A = (2*pi/0.012)^2*0.04

so

m = 110/((2*pi/0.012)^2*0.04)= 0.01 kg

d) m w^2 = k

k = 0.01*(2*pi/0.012)^2 = 2742 N/m

e) x(0) = 0.01

so

0.01 = 0.04*cos(phi)
phi = arcos(0.25)= 4.46 rad

f) max KE when x = 0

and max PE at max and min x values

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