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The following system is composed by two masses The first mass m, = 21 kg, moving...
The following system is composed by two masses . The first mass my - 20 kg,...
The following system is composed by two masses . The first mass my - 20 kg, moving horizontally on positive rightwards) . The second mass m2 - 2.5 kg, moving horizontally xx. positive rightwards) The first mass is connected to the ground on the left) by two springs, each with stiffness k-232 Nm. The second mass is connected to the first mass by another spring, also with stiffness -232 N/m. A harmonic force is applied to the first mass FIO)Foconut),...
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Ke...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Keep 3 significant figures, and omit units. Use m1 2 kg m2 4 kg k1 147 N/m k2 146 N/m K3 192 N/m F1 # 411 cos(0.50 N Note that the system is not damped. The homogeneous response does not decay to zero. The masses vibrates at three different frequencies...
A horizontal mass-spring system consists of a block (m=1.5 kg) on a frictionless to connected to...
A horizontal mass-spring system consists of a block (m=1.5 kg) on a frictionless to connected to a spring (k = 750 N/m). The system is initially at rest and is in equilibrium MI Second DIOCK (M=1.5 kg) approaches with a speed of 3.5 m/s and undergoes all inelastic collision with the first block (i.e.. they stick together after the collision). (a) What is the amplitude of the resulting simple harmonic motion (in cm)? (b) What is the angular frequency (w)...
An object of mass 24,000 kg, moving horizontally at 0.11 m/s is brought to a halt...
An object of mass 24,000 kg, moving horizontally at 0.11 m/s is brought to a halt by a spring, with a spring constant k = 268 kN/m. Assume the spring is initially at the equilibrium position, and find the magnitude of distance which the spring is compressed to bring the object to a halt. Assume energy is conserved. Give your answer in metres, to 2 sf.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
A system made up of a mass (m), attached to a spring of stiffness k [N/m]...
A system made up of a mass (m), attached to a spring of stiffness k [N/m] will oscillate to a specific amplitude (A) which will depend on an external force (F) and initial conditions. If all the variables involved are given in Table 1, formulate the necessary Pi groups to describe this behavior. Make sure you write the Pi groups using the parameters involved Parameter Variable Variable Units Amplitude A т Mass m kg Spring k N/m constant External F...
Two objects collide head-on (see figure below). The first object is moving with an initial speed...
Two objects collide head-on (see figure below). The first object
is moving with an initial speed of 7.99 m/s to the right and the
second object is moving with an initial speed of 10.00 m/s to the
left. Assuming the collision is elastic, m1 = 5.12 kg
and m2 = 6.15 kg,determine the final velocity of each
object. (Indicate the direction with the sign of your answer.
Positive is to the right, and negative is to the left.)
v1f
=...
An 8-kg block A slides in a vertical frictionless slot and is connected to a moving...
An 8-kg block A slides in a vertical frictionless slot and is connected to a moving support B by a spring of constant k=1.6 kN/m. If 8m is given as 150 mm, determine for small oscillations the following: (a) The equation of motion (EOM) (b) The natural frequency of vibration (c) The range of values of of such that the amplitude of the steady state force applied to the block via the spring is less than 120 N. 8.8., sin...
7. A block of mass 1.6 kg is moving across a smooth floor at 13.8 m/s...
7. A block of mass 1.6 kg is moving across a smooth floor at 13.8 m/s and encounters a second block (initially at rest) of mass 3.4 kg in a fully elastic collision. The second block is attached to a spring of k = 1250 N/m. Assume the spring to be massless and does not interfere with the collision. After the collision, the second block is under simple harmonic motion. Determine, a. The amplitude of oscillation b. The frequency of...
The following system is composed by two masses . The first mass my - 20 kg, moving horizontally on positive rightwards) . The second mass m2 - 2.5 kg, moving horizontally xx. positive rightwards) The first mass is connected to the ground on the left) by two springs, each with stiffness k-232 Nm. The second mass is connected to the first mass by another spring, also with stiffness -232 N/m. A harmonic force is applied to the first mass FIO)Foconut),...
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Keep 3 significant figures, and omit units. Use m1 2 kg m2 4 kg k1 147 N/m k2 146 N/m K3 192 N/m F1 # 411 cos(0.50 N Note that the system is not damped. The homogeneous response does not decay to zero. The masses vibrates at three different frequencies...
A horizontal mass-spring system consists of a block (m=1.5 kg) on a frictionless to connected to a spring (k = 750 N/m). The system is initially at rest and is in equilibrium MI Second DIOCK (M=1.5 kg) approaches with a speed of 3.5 m/s and undergoes all inelastic collision with the first block (i.e.. they stick together after the collision). (a) What is the amplitude of the resulting simple harmonic motion (in cm)? (b) What is the angular frequency (w)...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
A system made up of a mass (m), attached to a spring of stiffness k [N/m] will oscillate to a specific amplitude (A) which will depend on an external force (F) and initial conditions. If all the variables involved are given in Table 1, formulate the necessary Pi groups to describe this behavior. Make sure you write the Pi groups using the parameters involved Parameter Variable Variable Units Amplitude A т Mass m kg Spring k N/m constant External F...
Two objects collide head-on (see figure below). The first object
is moving with an initial speed of 7.99 m/s to the right and the
second object is moving with an initial speed of 10.00 m/s to the
left. Assuming the collision is elastic, m1 = 5.12 kg
and m2 = 6.15 kg,determine the final velocity of each
object. (Indicate the direction with the sign of your answer.
Positive is to the right, and negative is to the left.)
v1f
=...
An 8-kg block A slides in a vertical frictionless slot and is connected to a moving support B by a spring of constant k=1.6 kN/m. If 8m is given as 150 mm, determine for small oscillations the following: (a) The equation of motion (EOM) (b) The natural frequency of vibration (c) The range of values of of such that the amplitude of the steady state force applied to the block via the spring is less than 120 N. 8.8., sin...
7. A block of mass 1.6 kg is moving across a smooth floor at 13.8 m/s and encounters a second block (initially at rest) of mass 3.4 kg in a fully elastic collision. The second block is attached to a spring of k = 1250 N/m. Assume the spring to be massless and does not interfere with the collision. After the collision, the second block is under simple harmonic motion. Determine, a. The amplitude of oscillation b. The frequency of...
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