Question

In: Physics

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a...

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a maximum speed of 0.322 m/s. Calculate the period related to the motion of the mass. Calculate the amplitude. Calculate the maximum magnitude of the acceleration.

Expert Solution

The angular frequency of the oscillation is,

w = [k / m]^1/2

= [147 N/m / 0.770 kg]^1/2

= 13.8 rad/s

Thus, the period of the oscillation is,

T = 2(pi)/w

= 2(pi) / (13.8 rad/s)

= 0.4547 s

= 0.45 s

------------------------------------------------------------------------------

The amplitude of the oscillation is,

A = v_max/ w

= 0.322 m/s / 13.8 rad/s

= 0.023 m

-----------------------------------------------------------------------

Maximum acceleration is,

a_max = w²A

= (13.8 rad/s)²(0.023 m)

= 4.44 m/s²

genius_generous answered 4 months ago

A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with...

A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with an amplitude equal to half its natural length. The natural (un-stretched) length of the spring is 18.0 cm. (a) When submitting your work, sketch the figure below illustrating the position, and directly underneath that, the velocity of the mass as a function of time. Assume that x = 9.00 cm and v =0 m/s when t = 0.00 s. Label the amplitude A and...

A mass m = 3.27 kg is attached to a spring of force constant k =...

A mass m = 3.27 kg is attached to a spring of force constant k = 60.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A = 0.17 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle...

A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to...

A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to a table and is compressed down by 0.160 m. A)What upward speed can it give to a 0.360-kg ball when released? Express your answer to three significant figures and include the appropriate units. B) How high above its original position (spring compressed) will the ball fly? Express your answer to three significant figures and include the appropriate units.

a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and...

a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and damping constant 0.2 kg/s, is initially displaced 10 cm from equilibrium. (a) What is the natural frequency of oscillation? What is its period of oscillation? How long does it take for the amplitude to decrease to 10% of its starting value? How many oscillations have occurred in this time? What fraction of the initial energy remains after this time? b. Two traveling waves with...

1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is...

1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is pulled to the right 8.0 cm and released. The mass oscillates with a frequency of 6.0 Hz. If the mass is pulled to the right 16.0 cm before being released, what is the frequency? a. 6.0 Hz b. 3.0 Hz c. 1.5 Hz d. 12 Hz e. 24 Hz 2. A window loses power/heat energy through a pane of glass to the cold outside....

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released. (a) Find a formula for the position of the mass as a function of time. (b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce...

A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates...

A 0.59-kg object connected to a light spring with a force constant of 22.2 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. m/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. m/s (c) Determine the speed of the object as it passes the point 1.5 cm from the equilibrium position. m/s (d) For what value of x...

A 0.36-kg object connected to a light spring with a force constant of 23.4 N/m oscillates...

A 0.36-kg object connected to a light spring with a force constant of 23.4 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (b) Determine the speed of the object when the spring is compressed 1.5 cm. (d) For what value of x does the speed equal one-half the maximum speed?

1. A block of mass m attached to a spring with spring constant k oscillates horizontally...

1. A block of mass m attached to a spring with spring constant k oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5 cm. Taking m = 100 gm, and spring constant = 2.5 N/m, a) Find out the equations of position, velocity, and acceleration of the ball. Find also the total energy of the block when its velocity was 20 cm/s. b) Oscillating particles generate waves. What will be the equation of a...

A particle of mass 2.00 kg is attached to a spring with a force constant of...

A particle of mass 2.00 kg is attached to a spring with a force constant of 300 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 4.00 m. A 7.00 kg object is dropped vertically on top of the 2.00 kg object as it passes through its equilibrium point. The two objects stick together. (a) Does the amplitude of the vibrating system increase or decrease as a result of the collision? decreases increases no change (b)By...