A 1.5 kg mass is attached to a vertically oriented spring, stretching it 0.45 m. The mass is moved upwards 0.25 m from its equilibrium position and held. A 0.8 kg mass is added to the hanging mass and the total mass is released from rest. The frequency of oscillation is most nearly: 1.02 Hz 1.67 Hz O 1.47 Hz O 1.15 Hz O 0.74 Hz O 0.83 Hz O 0.96 Hz 0.60 Hz Clear selection
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- A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (rt + t/3). The velocity (in m/s) of the body at t = 1.0 s is О -14 +8.0 -8.0 O +14 О-5.0The position of a particle is given by the expression x = 2.00 cos (2.00nt + π/4), where x is in meters and t is in seconds. (a) Determine the frequency. Hz (b) Determine period of the motion. S (c) Determine the amplitude of the motion. m (d) Determine the phase constant. rad (e) Determine the position of the particle at t = 0.350 s. mA block on a spring obeys simple harmonic motion according to the equation: y(t) = (6.0cm) cos ((8.2rad/s) * t +0.18rad) What is the period of motion? O 6.0 cm O 0.77 s O 1.3 s O 8.2 rad/s ▶
- A spring is mounted vertically on the floor. The mass of the spring is negligible. A certain object is placed on the spring to compress it. When the object is pushed further down by just a bit and the released, one up/ down oscillation cycle occurs in 0.230s. However, when the object is pushed by 5.32 x 10-2 m from unstrained position to point P and then released, the object flies entirely off the spring. To what height above point P does the object rise in the absence of air resistance?Aweight is attached to a spring and is suspended from a ceiling so that it lies 30 cm from the ceiling when it is at rest. The spring is stretched so that the weight is 38 cm from the ceiling and is then released. It bounces up and down for a while. Each time it comes to the bottom of its bounce, the length of the stretch is 75% of the previous stretch. a) The period of each oscillation (bounce) is 1/2 second. Write an equation that represents the distance from the weight to the ceiling. b) Draw a graph of the function. c) Without doing any calculations, state the distance of the spring from the ceiling after 1 minuteThe equation of motion of a particle in simple harmonic motion is given by: x(t) = 0.2cos(wt), where x is in meters and t is in seconds. At x = 0, the particle's velocity is v = -1.256 m/s. The period of oscillation, T, equals: 0.25 sec 3 sec 1.5 sec 1sec 0.5 sec
- A 0.40-kg mass is attached to a spring with a force constant of k = 377 N/m, and the mass-spring system is set into oscillation with an amplitude of A = 1.9 cm. Determine the following. (a) mechanical energy of the system (b) maximum speed of the oscillating mass |m/s (c) magnitude of the maximum acceleration of the oscillating mass |m/s²1/2 Question 20 A 0.25-kg block oscillates on the end of the spring with a spring constant of200N/m. If the system has an energy of 6.0 J, then the amplitude of the oscillation is: ○ 4.9m O 6.9m O 0.24m O 0.17m 0 0.06mA block of mass m = 6.04 kg is attached to a spring with spring constant k = 1532 N/m and rests on a frictionless surface. The block is pulled, stretching the spring a distance of 0.145 m, and is held still. The block is then released and moves in simple harmonic motion about the equilibrium position. (Assume that the block is stretched in the positive direction.) (a) What is the frequency of this oscillation? Hz(b) Where is the block located 3.24 s after it is released? (Give the displacement from the equilibrium. Include the sign of the value in your answer.) m(c) What is the velocity of the mass at that time? (Indicate the direction with the sign of your answer.) m/s
- A mass is placed on a frictionless, horizontal table. A spring (k=175 N/mk=175 N/m), which can be stretched or compressed, is placed on the table. A 3.5-kg mass is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=7.0 cmx=7.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. Find the position, velocity, and acceleration of the mass at time t=3.00 st=3.00 s. x(t=3.00 s)=x(t=3.00 s)= cm v(t=3.00 s)=v(t=3.00 s)= cm/s a(t=3.00 s)=a(t=3.00 s)= cm/s2The position of a particle is given by the expression x = 6.00 cos (4.00nt + 2π/5), where x is in meters and t is in seconds. (a) Determine the frequency. Hz (b) Determine period of the motion. S (c) Determine the amplitude of the motion. m (d) Determine the phase constant. rad (e) Determine the position of the particle at t = 0.350 s. mA mass is placed on a frictionless, horizontal table. A spring (k=170 N/mk=170 N/m), which can be stretched or compressed, is placed on the table. A 3-kg mass is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=7.0 cmx=7.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. Find the position, velocity, and acceleration of the mass at time t=3.00 st=3.00 s. x(t=3.00 s)=x(t=3.00 s)= cm v(t=3.00 s)=v(t=3.00 s)= cm/s a(t=3.00 s)=a(t=3.00 s)= cm/s2