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5. (Vibrating Drum) The motion of a circular elastic membrane, such as the head of a drum, is gov...
The following model determines the vibration of a drum, specifically the vibration of the batter head,...
The following model determines the vibration of a drum,
specifically the vibration of the batter head, where the wave
equation is solved in polar coordinates.
u(r,t) is the height of a drum's surface at radius (r) and time
(t), which is relative to its position at rest.
c is a parameter which depends on surface density
(kg//m3) of the drum head, and with tension t (newtons)
applied to it.
Q1. Non-dimensionalise the following equation
Q2. From the question, what dimension...
(15 pts) Bessel functions and the vibration of a circular drum In polar coordinates, the Laplacia...
(15 pts) Bessel functions and the vibration of a circular drum In polar coordinates, the Laplacian is just like the Laplacian for the cylinder, but with the removed part เอ The structure of the Laplacian is what we call separable because the r and 0 terms are separate this allows us to solve certain physics problems on the disc by searching for solutions of the form f(r,0)-ar)b() The vibration of a circular drum head is described by 02t where u...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be mode...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be modeled by -27- 0<r<T, t>0 (PI) u(0, t) = u(, t ) t20 0 is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign. (2 points) (4 points) (b) Consider the separable solutions to (P1), ie., those of...
. (40 points: A membrane is stretched under tension r with uniform surface density o. (Small-amplitude)...
. (40 points: A membrane is stretched under tension r with uniform surface density o. (Small-amplitude) transverse displacements of this stretched membrane satisfy the wave equation కా - ఆ (10) Suppose the membrane is stretched in a rectangular frame lying in the plane z= 0, with side-lengths a, b. mitially stationary at all points, the membrane is struck at t-0 and thus set vibrating- 3.1. Show that e satisfies the following expression: veu)-ΣΣ..-ΣΣ Β.in may sin sin (wt] %3D (11)...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular drum lid is 1 au 1 ay c? + 012 72 302 for r € (0,R), 0€ (-2,7), and t > 0, and the boundary condition is (R, 6,t) = 0 for t>0 and -150<7. rar (4) You will search for a solution of the form v(r,0,t) = G(r) sin(30) cos(w t), (5) for a function G that satisfies the ODE m2 G" +rG'...
only f and g please 1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (suc...
only f and g please
1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (such as air) can be modeled by Fu 2&u 21 0rT t>0 at Ot2 (P1) u(0,t)u, t) 0 t20 Qu is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign (2 points) (4 points) (b) Consider the separable...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force pr...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
Need help with problems 1) b) ii), 2) b) and c), and 3) c) please! MAT All about Given a general line y mx + b, con...
Need help with problems 1) b) ii), 2) b) and c), and 3) c)
please!
MAT All about Given a general line y mx + b, convert to polar coordinates and solve for r. Check your answer with Desmos (add sliders for b, m). 1) a) rG b-mccre)- r -mces =Fcese, y=rtnb rsin6= mreese +h int-mr b Assume m<0 so that the line, the y-axis, and x-axis enclose a triangular area: b) Area e Xheigh) Use geometry to determine a...
Hi there can you please answer question part (b) (ii) - thank you Consider a test...
Hi there can you please answer question part (b) (ii) - thank
you
Consider a test particle of mass m orbiting in a Schwarzschild black hole of mass M. If the particle orbits at a speed uc and at a distance r > ., where c is the speed of light and . = 2GM/? the Schwarzschild radius, we can use the usual Newtonian central force equations of motion to analyse the orbit. The effective potential, however, needs to be...
Circular motion lab. explain how the rotating mass in this lab behaves like the passenger on the ...
circular motion lab. explain how the rotating mass in this lab
behaves like the passenger on the "barrel of fun" carnival ride?
what provides the centriprtal force for the experiment ? What
provides the centripetal force on the "barrel of fun"
ride?
Circular Motion The centripetal force acting orn the rotating mass is given by: 4T MR where M mass of the rotating mass R radius of orbit T period of orbit Procedure (1) Clamp the base of the apparatus...
The following model determines the vibration of a drum,
specifically the vibration of the batter head, where the wave
equation is solved in polar coordinates.
u(r,t) is the height of a drum's surface at radius (r) and time
(t), which is relative to its position at rest.
c is a parameter which depends on surface density
(kg//m3) of the drum head, and with tension t (newtons)
applied to it.
Q1. Non-dimensionalise the following equation
Q2. From the question, what dimension...
(15 pts) Bessel functions and the vibration of a circular drum In polar coordinates, the Laplacian is just like the Laplacian for the cylinder, but with the removed part เอ The structure of the Laplacian is what we call separable because the r and 0 terms are separate this allows us to solve certain physics problems on the disc by searching for solutions of the form f(r,0)-ar)b() The vibration of a circular drum head is described by 02t where u...
1. The motion of a vibrating string of length , with fixed endpoints, immersed in a fluid (such as air) can be modeled by -27- 0<r<T, t>0 (PI) u(0, t) = u(, t ) t20 0 is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign. (2 points) (4 points) (b) Consider the separable solutions to (P1), ie., those of...
. (40 points: A membrane is stretched under tension r with uniform surface density o. (Small-amplitude) transverse displacements of this stretched membrane satisfy the wave equation కా - ఆ (10) Suppose the membrane is stretched in a rectangular frame lying in the plane z= 0, with side-lengths a, b. mitially stationary at all points, the membrane is struck at t-0 and thus set vibrating- 3.1. Show that e satisfies the following expression: veu)-ΣΣ..-ΣΣ Β.in may sin sin (wt] %3D (11)...
+ (3) ar2 2. Recall from lectures that the governing PDE for vibrations of a circular drum lid is 1 au 1 ay c? + 012 72 302 for r € (0,R), 0€ (-2,7), and t > 0, and the boundary condition is (R, 6,t) = 0 for t>0 and -150<7. rar (4) You will search for a solution of the form v(r,0,t) = G(r) sin(30) cos(w t), (5) for a function G that satisfies the ODE m2 G" +rG'...
only f and g please
1. The motion of a vibrating string of length T, with fixed endpoints, immersed in a fluid (such as air) can be modeled by Fu 2&u 21 0rT t>0 at Ot2 (P1) u(0,t)u, t) 0 t20 Qu is a damping term, modelling the effect of at where c,>0. The term proportional to air resistance on the string. (a) Explain why the damping term has a minus sign (2 points) (4 points) (b) Consider the separable...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
Need help with problems 1) b) ii), 2) b) and c), and 3) c)
please!
MAT All about Given a general line y mx + b, convert to polar coordinates and solve for r. Check your answer with Desmos (add sliders for b, m). 1) a) rG b-mccre)- r -mces =Fcese, y=rtnb rsin6= mreese +h int-mr b Assume m<0 so that the line, the y-axis, and x-axis enclose a triangular area: b) Area e Xheigh) Use geometry to determine a...
Hi there can you please answer question part (b) (ii) - thank
you
Consider a test particle of mass m orbiting in a Schwarzschild black hole of mass M. If the particle orbits at a speed uc and at a distance r > ., where c is the speed of light and . = 2GM/? the Schwarzschild radius, we can use the usual Newtonian central force equations of motion to analyse the orbit. The effective potential, however, needs to be...
circular motion lab. explain how the rotating mass in this lab
behaves like the passenger on the "barrel of fun" carnival ride?
what provides the centriprtal force for the experiment ? What
provides the centripetal force on the "barrel of fun"
ride?
Circular Motion The centripetal force acting orn the rotating mass is given by: 4T MR where M mass of the rotating mass R radius of orbit T period of orbit Procedure (1) Clamp the base of the apparatus...
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