Problem 4: An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s.
a) [3 points] What is the angular frequency of the oscillations?
b) [3 points] If the mass of the object is 4 kg, what is the value of the spring constant, k?
c) [2 points] If the amplitude of the oscillations is 20 cm, what is the total energy of the spring mass system?
d) [4 points] Under the assumption above, what is the maximum velocity and acceleration of the object?
e) [5 points] Write down the formula for the position of the object as a function of time, x(t), assuming that its velocity is maximum at t = 0 going toward the positive direction. Identify the
value of all the constants that you use.
f) [3 points] Write down the formula for the position of the object as a function of time, x(t), assuming that its velocity is maximum at t = 0 going toward the positive direction. Identify the value of all the constants that you use. (If you use sine version for part (e), then you need to use the cosine version here, and vice versa)
Problem 4: An object is attached to a spring in such a way that it undergoes...
Problem 4: An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s. a) [3 points] What is the angular frequency of the oscillations? b) [3 points] If the mass of the object is 4 kg, what is the value of the spring constant, k? c) [2 points] If the amplitude of the oscillations is 20 cm, what is the total energy of the spring- mass system? d)...
Problem 4: An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s. a) [3 points] What is the angular frequency of the oscillations? b) [3 points] If the mass of the object is 4 kg, what is the value of the spring constant, k? c) [2 points) If the amplitude of the oscillations is 20 cm, what is the total energy of the spring- mass system? d)...
Problem 4 An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s a) 3 points] What is the angular frequency of the oscillations? b) (3 points) If the mass of the object is 4 kg, what is the value of the spring constant, k? c) (2 points] If the amplitude of the oscillations is 20 cm, what is the total energy of the spring- mass system? d)...
Problem 4: An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s. a) [3 points) What is the angular frequency of the oscillations? b) [3 points] If the mass of the object is 4 kg, what is the value of the spring constant, k? c) (2 points) If the amplitude of the oscillations is 20 cm, what is the total energy of the spring. mass system? d)...
A 2.5-kg object attached to an ideal spring with a force constant (spring constant) of 15 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 8 cm from the equilibrium position. (a) What is the frequency of the oscillations of the object? (b) Determine the maximum speed of the cart. (c) Find the maximum acceleration of the mass (d) How much total energy does this oscillating...
An object of mass 4 grams hanging at the bottom of a spring with a spring constant 3 grams per second square. Denote by y vertical coordinate, positive downwards and y 0 is the spring-mass resting position. TTA (a) Write the differential equation satisfied by this system Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. 2(yp)2+3/2y 2 Note: Write t for t, write y for...
A 2.00-kg object is free to slide on a horizontal surface. The
object is attached to a spring of spring constant 300 N/m , and the
other end of the spring is attached to a wall. The object is pulled
in the direction away from the wall until the spring is stretched
50.0 mm from its relaxed position. The object is not released from
rest, but is instead given an initial velocity of 2.50 m/s away
from the wall. Ignore...
Could you please answer all of the following questions? 1. A 3 kg object attached to a spring oscillates with an amplitude of 15 cm and a period of 2 s. At a time t = 0.5 s, the object's position is x = 9.1 cm. Determine a) the spring constant of the spring b) the total energy of the system (in joules) c) the maximum speed of the object d) the position of the object as a function of...
A 1.30-kg object is attached to a spring and placed on
frictionless, horizontal surface. A horizontal force of 21.0 N is
required to hold the object at rest when it is pulled 0.200m from
its equilibrium position......
Would you write out the intermediate steps, too, please?
A 1.30-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 21.0 N is required to hold the object at rest when it is pulled 0.200 m...
A 3.70 kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 19.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations (a) Find the force constant of the spring, N/m (b) Find the frequency of the oscillations Hz...