A mass-spring system executes simple harmonic motion. When the mass is at its ma

Question

A mass-spring system executes simple harmonic motion. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it is true? Its acceleration is zero. Its speed is zero. Its elastic potential energy is zero. Its kinetic energy is maximum. Its total mechanical energy is zero. What is the frequency of the wave shown in the figure? When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string? The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation? A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total mechanical energy of the system?

Explanation / Answer

9 problem

Given that

X(t) = 0.05 sin(126t)

so

V(t) = 126 * 0.05 cos (126t) = 6.3 cos(126t)

when t = 0, v = 6.3 m/s this is maximum velocity

Hence option A is correct choice.

10 problem

from the equation w = 126 rad/s

Therefore frequency f = w / 2 * pi

= 126 / 2 * 3.14

= 20. 6 Hz

Hence option B is correct choice

Problem 11

Acceleration = w2 A = 126 * 126 * 0.05 = 793.8 m/s2

Hence option D is correct choice.

Problem 12

v = w A = 126 * 0.05 = 6.3 m/s

Hence option C is correct choice.

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