## 1 Introduction  
The vehicle ride comfort and running safety depend, inter alia, on the technical condition of the shock absorbers used in vehicle suspension systems [1; 2; 3; 4; 5; 6]. With growing vehicles' time in service and mileage travelled, the effect of shock absorbers' functioning is weakening, and defects occur. Therefore, new, more effective methods of diagnosing their condition have been sought for many years [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. In particular, the on-vehicle test methods are desirable because of the short time and low cost of the test. However, the present-day diagnostic equipment should be suitable for testing the shock absorbers that would be susceptible to changes in the temperature of the working fluid [18; 19] and those of the controllable (e.g., magnetorheological [20]) type as well as the suspension systems with strong (and varying at that) sliding friction (e.g., in leaf springs [21]). The most modern testers are also required to offer reliable results of the inspection of shock absorbers installed in unique vehicles with electric motors placed in wheel hubs [22], where the unsprung mass would be significantly increased because of that. Among the numerous methods used, the 'forced vibration methods' have earned the widest acceptance [3; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. In such methods, the road wheel is forced to vibrate vertically with a frequency of 16-25 Hz, and then this frequency is lowered until the vibration disappears. Thus, the frequency range is'swept', which includes the natural frequencies of the sprung and unsprung masses supported by the suspension springs and tyres as elastic elements. This method makes use of the widely known fact that the system vibration is highly sensitive to damping in the resonance zone. At present, the most popular solutions are the EUSAMA method [1; 3; 5; 8; 9; 10; 11; 12; 16; 17; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33] and its significantly modified version named the 'phase angle method' proposed by the Hunter company [16; 17; 24; 28]. A somewhat less popular solution is the 'theta' method, where the suspension under test is assessed by means of a dimensionless damping coefficient (damping level), which is often denoted in the literature by symbol \(\vartheta\) (or \(\gamma\), \(\beta\), D, etc.). There are a few variants of this method [7; 8; 9; 10; 11; 12; 13; 14; 29; 30; 32; 33; 34], which lead to an indirect assessment of the main damping element, i.e., the shock absorber. This method is analysed by the authors of this paper in other publications [3; 25; 33; 35]. This article concerns the assessment of the usability of the phase angle method. In this solution (Figure 1), angle \(\Phi_{\text{ON}}\) of the phase shift between excitation \(\zeta\) (vertical displacement of the vibration plate) and force N at the contact between the road wheel (tyre) and the vibration plate [3; 36; 37; 10; 16; 17; 24; 26; 28; 30] is measured. The authors decided to compare the results of a theoretical analysis based on simulations with the results of experimental tests carried out on a prototype diagnostic test stand. The authors were interested in whether, in the phase angle method (as opposed to the EUSAMA method), the results of the diagnostic test can be expected to be independent of the non-linearity of the tested system (in particular, friction in the suspension) and the disturbing effect of the inertia of the plate forcing the vibrations. To do this, two 'quarter-car' models (linear and non-linear) were employed for the simulation, and two medium-class cars were used for the experimental tests. It was decided that, at first, the linear and non-linear models of the car placed on a diagnostic test stand (diagnostic tester) would be described, and only then the essence and properties of the phase angle method would be presented in detail. Such a sequence was chosen because it would be difficult to describe the method without using the notions presented in the description of the models.