Question

When a 0.350 kg package is attached to a vertical spring and lowered slowly, the spring...

When a 0.350 kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

a) Draw a diagram representing the scenario

b) Solve the equation symbolically (without numbers)

c) Solve the equation with numbers

d) State any relevant concepts

Homework Answers

Answer #1

given
m = 0.35 kg
delta_y = 12.0 cm = 0.120 m
let k is the spring constant.

a) sprring placed vertically and connected to a package.

b) in the equilibrium,

F_spring = Fg

k*delta_y = m*g

k/m = g/delta_y

angular frequency, w = sqrt(k/m)

and time period, T = 2*pi/w

= 2*pi/sqrt(k/m)

= 2*pi/sqrt(g/delta_y)

c) T = 2*pi/sqrt(9.8/0.120)

= 0.695 s

d) here the total mechaincal energy is concerved when the package makes oscillations.

when the pakcage is at rest initially the net force acting on the pakage is zero.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A block of mass m = 1.5 kg is attached to a massless, frictionless vertical spring...
A block of mass m = 1.5 kg is attached to a massless, frictionless vertical spring and stretches the spring by an amount y0 = 0.15m a)find the spring constant k of the spring b) the block is then pulled down by an additional 0.05m below its equilibrium position and is released. express the position of the block during its resulting simple harmonic motion using the equation y(t) = ymcos(wt+@). c) find the maximum acceleration fo the block A(m). d)...
When A 200 g block is attached to a vertical spring it is stretched by 10...
When A 200 g block is attached to a vertical spring it is stretched by 10 cm. If the block is then lifted 5 cm and released it will execute simple harmonic motion with a period of 0.3 s. (a) Find the force constant of the spring. (b) Find the mass of the block. (c) Find the amplitude of the motion. (d) What is the maximum speed of the block? (e) What is the speed of the block at the...
A 1.50-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal...
A 1.50-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 28.0 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. b.)Find the frequency of the oscillations. c.)Find the maximum speed of...
A block with mass 2 kg is attached to an ideal massless spring and undergoes simple...
A block with mass 2 kg is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.50 s. The surface is frictionless. The amplitude of the oscillation is 0.1 m. (a) What is the spring constant of the spring? (b) What is the total mechanical energy of the system (the spring and block system)? (c) What is the maximum speed of the block? (d) What is the speed of the block when the displacement...
A block with mass 2 kg is attached to an ideal massless spring and undergoes simple...
A block with mass 2 kg is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.50 s. The surface is frictionless. The amplitude of the oscillation is 0.1 m. (a) What is the spring constant of the spring? (b) What is the total mechanical energy of the system (the spring and block system)? (c) What is the maximum speed of the block? (d) What is the speed of the block when the displacement...
Question 1) Clearly solve: * A 0.50 kg mass attached to a spring undergoes a simple...
Question 1) Clearly solve: * A 0.50 kg mass attached to a spring undergoes a simple harmonic movement with an amplitude of 0.40 m and a period of 3.0 s. Find (a) the total energy of this oscillator (b) the maximum speed of the dough (c) the speed when the mass is at x = +0.20 m from the equilibrium position (d) the elastic potential energy stored in the spring when the mass moves at half its maximum speed
A 3.30-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal...
A 3.30-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 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 (c)...
A particle with mass 2.61 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 2.61 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.923 m and a duration of 129 s for 65 cycles of oscillation. Find the frequency, ?, the speed at the equilibrium position, ?max, the spring constant, ?, the potential energy at an endpoint, ?max, the potential energy when the particle is located 68.5% of the amplitude away from the equiliibrium position, ?, and the kinetic energy, ?, and...
1.A 1.10 kg block sliding on a horizontal frictionless surface is attached to a horizontal spring...
1.A 1.10 kg block sliding on a horizontal frictionless surface is attached to a horizontal spring with k = 490 N/m. Let x be the displacement of the block from the position at which the spring is unstretched. At t = 0 the block passes through x = 0 with a speed of 3.40 m/s in the positive x direction. What are the (a) frequency and (b) amplitude of the block's motion 2.A vertical spring stretches 13 cm when a...
with a complete solution A body of mass 2 gr attached to a vertical spring stretches...
with a complete solution A body of mass 2 gr attached to a vertical spring stretches it 1000/4 cm to reach an equilibrium position. When the body moves in the air it experiences a resistance opposite to its movement, proportional to its speed, with a damping constant d = 10 gr/sec. Approximate the acceleration of gravity by g = 1000 c m / s e c 2 . b. Find a differential equation of the form y ′′ = F...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT