10.1.2 The Equations Describing Simple Harmonic Motion

Question 1

The Equations Describing Simple Harmonic Motion

Answer 1

• The graphs of position, velocity, and acceleration versus time of an object in simple harmonic motion are sinusoidal and out of phase with one another.
• Applying Newton’s second law (F= ma) and Hooke’s law (F= -kx) to an object in SHM leads to the differential equation.
• The equation is the solution to the differential equation for SHM with the condition that

Question 2

Which of the following statements is true?

Answer 2

The particle executes simple harmonic motion with angular frequency sqrt(D^2q/m)

Question 3

A = -3.7m, w = 2.0 rad/s, and theta = 0.20 rad. What is the speed of the object when it is at x = -1.5 m?

Answer 3

6.8 m / s

Question 4

A mass m connected to a spring with spring constant k is free to slide horizontally on a frictionless surface. The system is set into simple harmonic motion with amplitude A = 1.3 m. If
m = 3.5 kg and k = 8.0 N / m, what is the maximum acceleration experienced by the mass?

Answer 4

3.0 m/s^2

Question 5

One of the springs on a city bus has been displaced by 0.500 m after hitting a bump and is oscillating with a frequency of 0.250 Hz. At
t = 0, a mass at the end of this spring is displaced 25.0 cm. Which of the following is the equation for the acceleration?

Answer 5

a(t) = -0.50 m (pi/2 rad/s)^2 * cos (pi/2 rad/s * t + pi/3)

Question 6

A beach ball with a mass of 0.08kg is bobbing up and down in a swimming pool in SHM with an amplitude of 0.14m. The maximum acceleration experience by the ball is 2.2 m/s^2. What is the ball’s maximum velocity?

Answer 6

0.55 m / s

Question 7

Consider a tuning fork of frequency 512 Hz and amplitude 1.50 mm. Which of the following are the accurate formulas for maximum displacement, maximum velocity, and maximum acceleration, respectively? Consider only the magnitude.

Answer 7

A, Aw, Aw^2

Question 8

A mass-spring system executes simple harmonic motion with period T. The mass is increased by a factor of seven, while the spring is replaced by another that is twice as long and three times as stiff (the spring constant k is three times larger than before). How does the period T′ of the new system compare to T ?

Answer 8

T’ = sqrt(7/3) T

Question 9

A spring will compress 5.60 cm when supporting a mass of 1,075 kg. This same spring is attached to a 1000.0 kg mass and laid horizontally on a frictionless surface. It is then stretched to 10.0 cm in the negative direction. If timing starts as the spring goes through equilibrium, which of the following describes the mass’ motion?

Answer 9

v = (-10.00)(13.7)sin(13.7t + pi/2)

Question 10

Consider a mass-spring system with a maximum displacement of A = 0.05 m. Its position function is shown the graph below. Which of the following is the velocity at 2.50 s?

Answer 10

0.00 m/s

Question 11

Which of the following is not an equation representing the force exerted by a spring during SHM?

Answer 11

F = -kAw sin (wt + theta)