The suspension of a vehicle is an assembly of coil springs that keep the vehicle from bouncing too much when riding over an irregular surface. Consider a motorcycle of mass 300 kg with one coil spring on each wheel, and the motorcycle's mass is evenly distributed over the two coils. The two coils are identical and have a spring constant of 5.5 × 10⁵ N/m each. The motorbike transports two 65 kg riders. Calculate the frequency of the oscillations of the motorcycle. Consider the motorcycle in simple harmonic motion.

A simple pendulum has a length of 1.35 m. The pendulum is displaced to one side by 5.60° and allowed to oscillate. Determine the time taken from the time it is launched to the time its acceleration is zero. 

Consider a mechanical system named "ResonantMech" that acts as a driven harmonic oscillator. When it operates at its resonance frequency of 419 Hz, the system's amplitude peaks at 25.7 F₀ / k. Determine the Q (quality factor) of this system. [Hint: $A_0=\frac{\left(\frac{F_0}{m}\right)}{\sqrt{{({\omega }^2-{\omega }_0^2)}^2+{\left(\frac{\omega b}{m}\right)}^2}}$ and $Q=\frac{m{\omega }_0}{b}$]

An oceanographer is studying wave patterns in the open sea from a research vessel. He observes that water wave crests pass a fixed point on the vessel every 5.0 seconds. He also measures the distance from one crest to the next to be 20 meters. Determine the velocity of these water waves.

A guitar fretboard is about 0.65 m in length. A guitar learner plucks a string (made of bronze) of the guitar at one of its endpoints. This creates a transverse wave in the string that takes 2.6 × 10^-3 s to bounce off the other end of the string and reach back at the same endpoint. Given that the diameter of the string is 2.6 × 10^-2 cm, calculate the tension in the string.

[Assume that Bronze has a density of 8800 kg/m³.]

A sound wave travels through a railway track made of steel. From the table below, estimate the speed with which sound travels through the railway track.

Some physics students are studying waves and vibrations. In the laboratory, they created a wave on a rope to observe its characteristics. The wave is described by the equation P (x, t) = 0.02 sin (40x - 1500t). Here, all the quantities are given in SI units. Find an expression for a wave having the same frequency, amplitude, and wavelength but that travels in the opposite direction.

A rope is fixed at one end and is experiencing a transverse wave traveling to the left. This wave can be represented by the equation y(x,t) = 2.5 mm sin (πx+2πt+2π/3), where x is measured in meters and t is measured in seconds. The rope has a mass per unit length of 8.0 g/cm. Determine the maximum vertical speed of a small section of the rope.

A thin steel cable with 2.0 mm diameter is hooked up to a vibrating device, which exerts a tension of 8.5 N on the cable. The device vibrates at a frequency of 70.0 Hz, producing waves in the cable with an amplitude of 0.50 cm. Calculate the power output of this device, assuming the waves do not reflect back along the cable. (The density of steel is ρ_steel=7800 kg/m³).

A bug on the surface of a pond is observed to move up and down a total vertical distance of 0.20 m, lowest to highest point, as a wave passes. What is the amplitude of the wave?

An online tune generator creates sine sound waves in the air with a displacement amplitude of 0.04 mm at f₁ = 200 Hz and f₂ = 20 kHz. What is the pressure amplitude (p_max) at each frequency?  Specify, under these conditions, if these sound frequencies are harmful to human hearing. The pressure variation that corresponds to the harm threshold is 30 Pa. 

Two transverse pulses are traveling towards each other through a slinky. Pulse A is moving to the right, and Pulse B is moving to the left. When the pulses intersect, the slinky is completely straight. Discuss what happens to the energy of the pulses at this point.

Determine the speed of the traveling waves on a 75-cm banjo string that is fixed at both ends and resonates at frequencies of 2.2, 2.5, and 2.8 kHz within the range of 2.0 to 3.0 kHz.

A string, fixed at its ends, oscillates according to the equation y(x,t) = (3 cm) sin [(π rad/cm) x]sin[(200π rad/s)t]. What is the speed of the two traveling waves that form this standing wave pattern?

A 450 Hz pure sound wave is directed toward the upper end of a graduated glass cylinder held straight up. The glass cylinder of 130 cm in height is totally filled with oil and has a tap at the base. The oil is at room temperature. The oil is drained gently from the tap. We are expecting that standing waves will be generated inside the cylinder at specific oil levels, h. The level h is measured from the base. Calculate the values of h.

at will be the beat frequency heard when two guitar strings, initially tuned to the same frequency of 298 Hz, are played together after the tension in one string is decreased by 3.0%? [Hint: $f^{\prime}=\frac{1}{\lambda}\sqrt{\frac{F_{T}^{\prime}}{\frac{m}{L}}}$ ], where $f^{\prime }$ is the new frequency, and $F_T^{\prime }$ is the new tension.

A 2.0 W, 2.5 KHz sound emitter is released 180 m above a detector. The atmospheric temperature is 22°C. Find the i) frequency and ii) the sound intensity level detected by the detector 5.5 s from the instant the emitter was released.

At room temperature (25°C), a 2.5 kHz sound wave causes ±0.060% fluctuation in pressure relative to atmospheric pressure. Calculate the peak speed of vibrating gas molecules in mm/s.

A 1.4 m high container is full of oil. Determine the pressure difference in mm-Hg between the top and bottom of the container given that the density of the oil is 7.5 × 10² kg/m³ and 1.0 mm-Hg = 130 N/m².

What is the area of the input piston if a hydraulic press is used to lift a heavy crate with a mass of 970 kg to a height of 40 cm, with an output piston diameter of 44 cm and an input force of 420 N?

A water tank on the ground level supplies water to a building. The topmost floor of the building is 55 m above the ground. What should be the minimum gauge pressure in the tank so that water reaches this topmost floor?

An open-tube water manometer, with a water density of 1000 kg/m³, is used to measure the pressure of a gas in a tank. The atmospheric pressure is given as 1025 mbar. What will be the absolute gas pressure in pascals if the water column in the open tube is 10 cm lower than the water in the tube connected to the tank?

Determine what the maximum cargo weight value is that a spherical air balloon filled with hydrogen, which has a density of 0.08375kg/m³, can lift up at 0°C and 1 atm pressure. The balloon has a radius of 8.15 m, and the combined mass of the balloon's structure and skin is 880 kg. Assume that the buoyant force on the cargo itself is negligible.

A 3.2 m long pipe with a radius of 12.7 mm is attached to a tank. The tank is filled with water at 25°C. Water flows through the pipe at different rates depending on the water height above the pipe in the tank. Calculate the greatest volume flow rate in m³/h at which the flow will be laminar.

A pipeline consists of sections of different cross-sections.  Oil flowing in the pipeline fills all cross-sections completely. A section Y of the pipeline has a cross-sectional area of 1.15 m² and the velocity magnitude at that point is 1.8 m/s. Determine the volume delivered to a tank every hour at the pipeline's terminal.