A particle of mass m is located at a one-dimensional potential, a b U(x) x2 - Where the period of positive oscillations effected by the particle with respect а, b are constants. Show that small to the equilibrium position is T = 4n/2ma³ /b4
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- Problem 2 ( ). A very light spring with spring constant 200 N/m hangs vertically the ceiling with equilbrium length Lo = 6 cm. When a 300 g mass is attached to the end spring, the mass-spring system extends to a new equilibrium length. Lo y = 0 (a) What is the length L of the spring when the mass-spring system is in equilibrium? If the mass is released from rest with the spring at its original equilibrium length (b) 6 cm, find the velocity of the mass when the spring has stretched to the length L you found in (a). 000000A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)7. A block of mass m slides with constant velocity v down a plane inclined at 0 with the horizontal. During the time interval At, what is the magnitude of the energy dissipated by friction? (a) mgv At tan 0 (b) mgv At sin 0 (c) 1/2 mv3 At (d) The answer cannot be determined without knowing the coefficient of kinetic friction.
- answer vii) onwards and dont use chatgpt thank you!Using the spring force, F = -kx, calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity c) of the mass? d) At what x coordinate does this maximum velocity occur?The torce reguired to compress a non-standard spring as a qunction as. 04 displacement isgiven by the equation F(X) = -Asin (bx)t Kx, where A= 1L0N, b= 1l rad|m, and k- 58 NIm.0 IE M Part A:Enter a general equation in terms 07 the given I iiar 1iaNariables 7or the work requircol to comeress this spring7om positionx, txa: part Bi calculate the work done injouicr as the spring Is come ressed prmi itt bot Woe1=? Arom x=0t X,=38 cm. joulEJ asthe Spring Is Partc: calculate the Workdone in compressed 7rom x1=38cm To xg=69 cm