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Consider a mass-spring system shown below with a hard spring. That is, it requires more force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
SYSTEMS Please be detailed. fex) = sin son crox) Problem 1: (25pts) Linearization Consider a mass...
SYSTEMS
Please be detailed.
fex) = sin son crox) Problem 1: (25pts) Linearization Consider a mass held by a nonlinear spring shown below. The equation of motion is given by f'(x) 3 Sin (20x) COS(20x) 20 + sinº (20) = 9, where is the stretch in the spring in meters, k is the nonlinear spring constant, m is the mass of the block, and g is the gravitational acceleration. Note that the argument of sin is in radians. This equation...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
help me with this Consider the vibration of mass spring system given by the initial value...
help me with this
Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
AP1. Consider the pendulum system shown below, where L = 0.7 meters, m = 1.5 kg,...
AP1. Consider the pendulum system shown below, where L = 0.7 meters, m = 1.5 kg, g = 9.81 m/s and e(t) is measured in radians. Pivot point Massless rod ! Lom, mass a. Show (by hand) that the motion of the pendulum is represented by the following dynamic equation: (t) + sin(()) = 0 b. Note that the differential equation above is nonlinear. When the equation is linearized about the equilibrium point (0) = 0, the linear time-invariant (LTI)...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
(a) A mass weighing w pounds stretches a spring spring as shown in the figure below foot and stre...
(a) A mass weighing w pounds stretches a spring spring as shown in the figure below foot and stretches a different spring foot. The two springs are attached in series and the mass is then attached to the double rigid support Assume that the motion is free and that there is no damping force present. Determine the equation of motion if the mass is initially released at a point 1 foot below the equilibrium position with a downward veloity of's...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
A 20 g mass-spring system is suspended vertically. If 20 g is added, it stretches 5...
A 20 g mass-spring system is suspended vertically. If 20 g is
added, it stretches 5 cm. (Assume the mass of the spring is
negligible)
A) The spring constant is
________ N/m.
From equilibrium position give mass-spring a speed of
1.2 m/s.
B1) Period of oscillation is ______ s
B2) Maximum speed of the the spring-mass system is _______
m/s.
B3) The equation of motion of the oscillating spring is
_______.
B4) The maximum kinetic energy of the spring is...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
SYSTEMS
Please be detailed.
fex) = sin son crox) Problem 1: (25pts) Linearization Consider a mass held by a nonlinear spring shown below. The equation of motion is given by f'(x) 3 Sin (20x) COS(20x) 20 + sinº (20) = 9, where is the stretch in the spring in meters, k is the nonlinear spring constant, m is the mass of the block, and g is the gravitational acceleration. Note that the argument of sin is in radians. This equation...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
help me with this
Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
AP1. Consider the pendulum system shown below, where L = 0.7 meters, m = 1.5 kg, g = 9.81 m/s and e(t) is measured in radians. Pivot point Massless rod ! Lom, mass a. Show (by hand) that the motion of the pendulum is represented by the following dynamic equation: (t) + sin(()) = 0 b. Note that the differential equation above is nonlinear. When the equation is linearized about the equilibrium point (0) = 0, the linear time-invariant (LTI)...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
(a) A mass weighing w pounds stretches a spring spring as shown in the figure below foot and stretches a different spring foot. The two springs are attached in series and the mass is then attached to the double rigid support Assume that the motion is free and that there is no damping force present. Determine the equation of motion if the mass is initially released at a point 1 foot below the equilibrium position with a downward veloity of's...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
A 20 g mass-spring system is suspended vertically. If 20 g is
added, it stretches 5 cm. (Assume the mass of the spring is
negligible)
A) The spring constant is
________ N/m.
From equilibrium position give mass-spring a speed of
1.2 m/s.
B1) Period of oscillation is ______ s
B2) Maximum speed of the the spring-mass system is _______
m/s.
B3) The equation of motion of the oscillating spring is
_______.
B4) The maximum kinetic energy of the spring is...
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