Question

Can you please answer both questions, Y=0

Problem3 A (2+0.1y) kg block attached to a spring undergoes simple harmonic motion described by x (30 cm) cos[(6.28 rad/s)t + /4) Determine (a) the amplitude, (b) the spring constant, (c) the frequency, (d) the maximum speed (e) maximum acceleration of the block, and (e) the total energy of the spring-block. of the block Problem 4 A block attached to a spring, undergoes simple harmonic motion with a period of 1.5 + y) cm. The mechanical energy of the spring-block system is 2 J. What is th f (10 e mass of the block?

Answer 1

(3) The displacement is given by the equation,

Cmm

(a) The amplitude is the maximum displacement the block undergoes, therefore the amplitude is 30 cm.

(b) The angular frequency of oscillation of the block is,

$\omega = 6.28 \, rad/s$

We know that,

2 0.1y

(c) The frequency can be calculated from the angular frequency, this gives,

k 78.88 + 0.3944yy/m

$\omega = 2 \pi f \Rightarrow f = \frac{\omega}{ 2 \pi}$

6.28 f =-= 0.99 H

(d) Differentiating the above displacement function we get the velocity as,

.r(t)--(30 × 6.28)siri (6.28t + π/4)--188.4sin (6.28t + π/4) cm

Hence the maximum speed attained is 188.4 cm/s.