Question

A 0.43 kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing. On a coordinate plane with a horizontal axis labeled t(s) and a vertical axis labeled x(m) there is one item, a curve that begins at the origin, (0, 0), curves up to a maximum at (1, 0.200), then down through (2, 0) to a minimum at (3, -0.2), then ends at (4, 0). There are lines connecting the tickmarks on the graph to the values of the points given. Determine the following.

(a) amplitude A of the motion 0.2 m

(b) angular frequency ω 1.57 rad/s

(c) spring constant k 1.06 N/m

(d) speed of the object at t = 1.00 s 0 m/s (e) magnitude of the object's acceleration at t = 1.00 s m/s2

I need help with (d) especially

Answer 1

a) Amplitude, A = Ymax = 0.2 m

b) T = 4 sec

f = 1/4 = 0.25 Hz

w = 2 pi f = 1.57 rad/s

c) m w^2 = k

k = 0.43 * 1.57^2 =1.06 N/m

d) at t = 1sec

particle is at extreme poisition hence speed = 0

OR equation of motion, x = A sin(wt) = 0.2 sin(1.57t)

at v = dx/dt = 0.2*1.57 cos(1.57t) = 0.314 cos(1.57)

and cos(1.57) = 0

e) a = dv/dt = - 0.49 sin(1.57t) = 0.49 m/s^2

Or a = F/m = kA/m = (1.06 x 0.2)/(0.43) = 0.49 m/s^2