A box on a frictionless surface is attached to a spring on one end. The box is p

Question

A box on a frictionless surface is attached to a spring on one end. The box is pulled to the right, which stretches the spring as shown in the figure. The is released from rest at t = 0sec. It then oscillates along the surface with a period of 2.0 sec and a maximum speed of 50 cm/s. Take positions to the right of the equilibrium position to have positive values of x, as shown in the figure. Which of the following equations best describes the displacement of the box as a function of time, x(t). where x0 is the amplitude of the oscillation, and omega its angular frequency? x(t) = -x0 sin(omega t) x(t) = x0 sin(omega t) x(t) = x0 cos(omega t) x(t) = -x0 cos(omega t) Which of the following equations best represents the velocity of the box as a function of time, v(t)? v(t) = -x0 omega sin(omega t) v(t) = -x0 omega cos(omega t) v(t) = x0 cos(omega t) v(t) = -x0 cos(omega t) What is the amplitude of the oscillation of the box? 16 cm 160 cm 120 cm 12 cm 1.2 cm What is the position of the box at t = 5.25 sec?

Explanation / Answer

7) displacement of the box

x(t) = x cos(wt) OPTION 'C'

8) velocity of the box

v(t)= -xw sin(wt) OPTION 'D'

9) max speed = 50 cm/s

time period = 2 sec

=> frequency = 0.5 Hz

V max = 2*pi*f*A

where A is amplitude

=> 50 = 2*pi*0.5*A

=> A = 15.915494 cm

approx 16cm OPTION 'A'

10) AT t=5.25 sec block is moving in postive x direction towards equillibrium posotion .

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