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9. The picture on the right shows a bead of mass m sliding on a frictionless...
4. A bead of mass m slides on a frictionless wire bent into the shape of...
4. A bead of mass m slides on a frictionless wire bent into the shape of a parabola 2 yd as shown above. Gravity acts in the negative y direction. A spring with elastic constant k and rest length d/2 connects the bead to a fixed anchor at the point (0, -d). Find the frequency of small oscillations about equilibrium. Hint: Find the potential energy Uof the bead. Then expand Uin series, keeping only the leading x2 term, to obtain...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
The figures to the right show a rod with length, l, and mass, M, on a frictionless table rotated an angle θ from the horizontal. It is fix to the table by a pin Sring through its center of mass...
The figures to the right show a rod with length, \(l\), and mass, \(M\), on a frictionless table rotated an angle \(\theta\) from the horizontal. It is fix to the table by a pin through its center of mass, and can rotate freely about this pin. On the two ends of the rod are connected identical springs with spring constant, \(k\), and the equilibrium position of the springs is when \(\theta=0\). In this problem, \(\theta \ll 1 \mathrm{rad}\), and the...
please advice into missing information. A bead of mass m is constrained to slide without friction...
please advice into missing information.
A bead of mass m is constrained to slide without friction on a circular hoop of radius R. The hoop is oriented vertically and is attached to a motor that rotates it at a constant angular speed o, as shown in the attached figure. The bead experiences a constant gravitational force directed downward, given as mg. Answer the following questions: (a) Find the Lagrangian for this system using appropriate variables. (b) Find the effective potential....
The figure shows block 1 of mass 0.265 kg sliding to the right over a frictionless...
The figure shows block 1 of mass 0.265 kg sliding to the right over a frictionless elevated surface at a speed of 8.85 m/s. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant 1166 N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of 0.135 s, and block 1 slides off the opposite end of the elevated surface,...
Figure 15-34 shows block 1 of mass 0.200 kg sliding to the right over a frictionless elevated sur...
Figure 15-34 shows block 1 of mass 0.200 kg sliding to the right over a frictionless elevated surface at a speed of 8.00 m/s. The block undergoes an elastie collision with stationary block 2, which is attached to a spring of spring constant 1208.5 N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of 0.140 s, and block 1 slides off the opposite end of the elevated sturface,...
Problem 1 A block of mass m is sliding on a frictionless, horizontal surface, with a...
Problem 1 A block of mass m is sliding on a frictionless, horizontal surface, with a velocity vi . It hits an ideal spring, of spring constant k, which is attached to the wall. The spring compresses until the block momentarily stops, and then starts expanding again, so the block ultimately bounces off (see Example 5.6.2). (a) Write down an equation of motion (a function x(t)) for the block, which is valid for as long as it is in contact...
Problem 1 A block of mass m is sliding on a frictionless, horizontal surface, with a...
Problem 1 A block of mass m is sliding on a frictionless, horizontal surface, with a velocity vi . It hits an ideal spring, of spring constant k, which is attached to the wall. The spring compresses until the block momentarily stops, and then starts expanding again, so the block ultimately bounces off (see Example 5.6.2). (a) Write down an equation of motion (a function x(t)) for the block, which is valid for as long as it is in contact...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A t O the trolley carries a simple pendulum of length I with a body of mass m at its end. Two equal springs, each of stiffness k, are attached to the trolley and to the fixed walls. By using the independent co-ordinates x and ? as shown in the figure, determine, for the small free oscillations, the equations of motion. If M-100 kg, m-10...
A mass m is on a horizontal frictionless surface and is attached to an ideal horizontal...
A mass m is on a horizontal frictionless surface and is attached to an ideal horizontal spring of spring constant k. The equilibrium position of the free end of the spring is at x = 0. The displacement of the mass by P⃗ begins and ends with the mass at rest.the displacement begins at position xi and ends at position xf. Select all true statements.a) Wp=-Ws b)=integration(kxdx) c)Wp=0 d)Wspring=0 e)Ws= integrate(-kxdx) f)P(x)=kx
4. A bead of mass m slides on a frictionless wire bent into the shape of a parabola 2 yd as shown above. Gravity acts in the negative y direction. A spring with elastic constant k and rest length d/2 connects the bead to a fixed anchor at the point (0, -d). Find the frequency of small oscillations about equilibrium. Hint: Find the potential energy Uof the bead. Then expand Uin series, keeping only the leading x2 term, to obtain...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
The figures to the right show a rod with length, \(l\), and mass, \(M\), on a frictionless table rotated an angle \(\theta\) from the horizontal. It is fix to the table by a pin through its center of mass, and can rotate freely about this pin. On the two ends of the rod are connected identical springs with spring constant, \(k\), and the equilibrium position of the springs is when \(\theta=0\). In this problem, \(\theta \ll 1 \mathrm{rad}\), and the...
please advice into missing information.
A bead of mass m is constrained to slide without friction on a circular hoop of radius R. The hoop is oriented vertically and is attached to a motor that rotates it at a constant angular speed o, as shown in the attached figure. The bead experiences a constant gravitational force directed downward, given as mg. Answer the following questions: (a) Find the Lagrangian for this system using appropriate variables. (b) Find the effective potential....
The figure shows block 1 of mass 0.265 kg sliding to the right over a frictionless elevated surface at a speed of 8.85 m/s. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant 1166 N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of 0.135 s, and block 1 slides off the opposite end of the elevated surface,...
Figure 15-34 shows block 1 of mass 0.200 kg sliding to the right over a frictionless elevated surface at a speed of 8.00 m/s. The block undergoes an elastie collision with stationary block 2, which is attached to a spring of spring constant 1208.5 N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of 0.140 s, and block 1 slides off the opposite end of the elevated sturface,...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A t O the trolley carries a simple pendulum of length I with a body of mass m at its end. Two equal springs, each of stiffness k, are attached to the trolley and to the fixed walls. By using the independent co-ordinates x and ? as shown in the figure, determine, for the small free oscillations, the equations of motion. If M-100 kg, m-10...
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