Suppose a 1 kg mass is attached to the end of a string that is stretched...

Suppose a 1 kg mass is attached to the end of a string that is stretched 0.2 m by a force of 500 N (newtons). An exterior force F0 cos 50t acts on the mass. Find the position function x(t) if the initial conditions are given by x(0) = 0, x′(0) = 50.

Expert Solution

Colby Messinger answered 1 year ago

1.A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a...

1.A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum linear speed can the mass have if the string is not to break? A.370 m/s B.22 m/s C.19 m/s D.29 m/s 2.A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s2. What is the angular speed of the wheel?...

A string is tied to the ceiling and is attached to a 50 kg mass that...

A string is tied to the ceiling and is attached to a 50 kg mass that hangs down freely. The 1.5-m-long string has a mass of 3.7 grams. a. What is the speed of waves that exist on the string? b. What is the frequency of the fundamental (m=1) harmonic of standing waves on the string? c. What is the frequency of the 3rd (m=3) harmonic of standing waves on the string? d. How much mass would have to be...

A stretched string fixed at each end has a mass of 43.0 g and a length...

A stretched string fixed at each end has a mass of 43.0 g and a length of 7.20 m. The tension in the string is 47.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Answer from smallest to largest distance from one end of the string.) nodes ______m ______m ______m ______m antinodes ______m ______m ______m (b) What is the vibration frequency for this harmonic? Hz

A block with mass 5 kg is attached to the end of a horizontal spring with...

A block with mass 5 kg is attached to the end of a horizontal spring with spring constant 200N/m. The other end of the spring is attached to a wall. The spring is stretched 10cm in the positive directions from its equilibrium length. Assume that the block is resting on a frictionless surface. A) When the spring is fully stretched, what is the magnitude of the force from the spring on the block? B) We then release the block, letting...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

A small block with mass 0.350 kg is attached to a string passing through a hole...

A small block with mass 0.350 kg is attached to a string passing through a hole in a frictionless, horizontal surface. The block is originally revolving in a circle with a radius of 0.500 m about the hole with a tangential speed of 1.50 m/s, uniformly. Consider the block as a particle. Moment of inertia of a particle is I=mr2, where r is the radius of the circle. Of course a tension force of the string is holding the block...

A box of mass m = 10.0 kg is attached to a rope. The other end...

A box of mass m = 10.0 kg is attached to a rope. The other end of the rope is wrapped around a pulley with a radius of 15.0 cm. When you release the box, it begins to fall and the rope around the pulley begins to unwind, causing the pulley to rotate. As the box falls, the rope does not slip as it unwinds from the pulley. If the box is traveling at a speed of 2.50 m/s after...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm under the influence of the weight of this mass. Now a periodic force is applied external of F (t) = 200 cos (vt) on the mass, which was initially in static balance. Disregarding all friction, get a relationship for position of the mass as a function of time, x (t). Also determine the value of ω which will cause resonance to occur

A mass, m=1.4 kg of negligible size, is attached at the end of a uniform rod...

A mass, m=1.4 kg of negligible size, is attached at the end of a uniform rod of length L= 0.99 mm which has mass M= 1.9 kg . What is the moment of inertia of this arrangement if it is to rotate at an axis located at a distance 0.39*L from the end of the rod opposite to the mass, m? (At approximately the point marked with an 'X'.) Calculate the moment of inertia of the rod-mass system given that...

1. A thin taut string of mass 5.00 g is fixed at both ends and stretched...

1. A thin taut string of mass 5.00 g is fixed at both ends and stretched such that it has two adjacent harmonics of 525 Hz and 630 Hz. The speed of a traveling wave on the string is 168 m/s. a.Determine which harmonic corresponds to the 630 Hz frequency. b.Find the linear mass density of this string. c.Find the tension in the string.

Question